One World Actuarial Research Seminar



Recording of last talk

Speaker: Peng Shi (University of Wisconsin, USA)
Title: A Copula Model for Marked Point Process with A Terminal Event: An Application in Dynamic Prediction of Insurance Claims
Abstract (click to expand) Accurate prediction of an insurer’s outstanding liabilities is crucial for maintaining the financial health of the insurance sector. This study is driven by the imperative for insurers to dynamically forecast unpaid losses using the granular transaction data on individual claims. We introduce a copula-based point process framework to model the recurrent events of payment transactions from an insurance claim, where the longitudinal payment amounts and the time-to-settlement outcome are formulated as the marks and the terminal event of the counting process, respectively. The dependencies among the three components are characterized using the method of pair copula constructions. We further develop a stage-wise strategy for parameter estimation and illustrate its desirable properties with numerical experiments. Real data applications further illustrate that our proposed joint model enhances the insurer's decision making in claims management and risk financing operations.


Format

  • Talk: 50min Q&A: 20min
  • Wednesday fortnightly
  • Rotating time slots to accommodate researchers from all time zones
  • How to join

  • We will use Zoom.
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  • Upcoming Talks

    Date & Time Speaker Title Misc
    14 February 2024 3pm (UTC)
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    Peng Shi (University of Wisconsin, USA) A Copula Model for Marked Point Process with A Terminal Event: An Application in Dynamic Prediction of Insurance Claims
    Abstract (click to expand) Accurate prediction of an insurer’s outstanding liabilities is crucial for maintaining the financial health of the insurance sector. This study is driven by the imperative for insurers to dynamically forecast unpaid losses using the granular transaction data on individual claims. We introduce a copula-based point process framework to model the recurrent events of payment transactions from an insurance claim, where the longitudinal payment amounts and the time-to-settlement outcome are formulated as the marks and the terminal event of the counting process, respectively. The dependencies among the three components are characterized using the method of pair copula constructions. We further develop a stage-wise strategy for parameter estimation and illustrate its desirable properties with numerical experiments. Real data applications further illustrate that our proposed joint model enhances the insurer's decision making in claims management and risk financing operations.
    13 March 2024 3pm (UTC)
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    Marie-Pier Côté (Université Laval, Canada) TBA
    Abstract (click to expand) TBA
    10 April 2024 3pm (UTC)
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    Christian Genest (McGill University, Canada) TBA
    Abstract (click to expand) TBA
    24 April 2024 3pm (UTC)
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    Mario Ghossoub (University of Waterloo, Canada) TBA
    Abstract (click to expand) TBA
    08 May 2024 3pm (UTC)
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    Corina Constantinescu (University of Liverpool, UK) TBA
    Abstract (click to expand) TBA
    22 May 2024 8am (UTC)
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    Jae Kyung Woo (University of New South Wales, Australia) TBA
    Abstract (click to expand) TBA
    05 June 2024 3pm (UTC)
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    Karim Barigou (Université Laval, Canada) TBA
    Abstract (click to expand) TBA

    Past Talks

    Date & Time Speaker Title Misc
    17 January 2024 3pm (UTC)
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    Claudia Czado and Ariane Hanebeck (Technical University of Munich, Germany) Dependence models for mortalities using a copula state-space approach
    Abstract (click to expand) We investigate how the COVID-19 pandemic has affected mortality experience of major causes, and more importantly how COVID-19 has changed the dependence structure across these causes. This enables us to gain more insights into the potential impact of COVID-19 on future life expectancy, and conduct scenario-based projections. For this we propose a dynamic copula state space approach, which quantifies and visualizes the joint dynamics across major causes of death, both before and during the pandemic. Based on US weekly mortality data from January 2015 to November 2022, we find that COVID-19 has elevated the mortality level for a majority of causes, and has changed the dependence structure across these causes. This work is joint with Han Li, Centre for Actuarial Studies, Department of Economics, The University of Melbourne, Australia.
    31 January 2024 9am (UTC)
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    Eric Ulm (Victoria University of Wellington, New Zealand) Analytic Valuation of Guaranteed Lifetime Withdrawal Benefits
    Abstract (click to expand) We exhibit and solve the partial differential equation that must be satisfied by Guaranteed Lifetime Withdrawal Benefits (GLWB) embedded in variable annuity contract when the benefit base for the withdrawals is the continuous running maximum of the fund (i.e. a ratchet GLWB) and the force of mortality is constant. We show that the fair fees are significantly higher in this case and highly sensitive to the withdrawal rate, risk-free rate, mortality rate and volatility. The value of the ratchet GLWB including fees is smaller when fund performance is poor and larger when fund performance is good which may make these policies less desirable to risk-averse policyholders.

    Talks in 2023
    Date & Time Speaker Title Misc
    18 January 2023 4pm (UTC)
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    Mogens Steffensen (University of Copenhagen, Denmark) Optimal consumption, investment, and insurance under state-dependent risk aversion
    Abstract (click to expand) We formalize a consumption-investment-insurance problem with the distinction of a state-dependent relative risk aversion. The state-dependence refers to the state of the finite state Markov chain that also formalizes insurable risks such as health and lifetime uncertainty. We derive and analyze the implicit solution to the problem, compare it with special cases in the literature, and illustrate the range of results in a disability model where the relative risk aversion is preserved, decreases, or increases upon disability. We also discuss whether the approach is appropriate to deal with uncertainty in relative risk aversion and consider some alternative ideas.
    Host:TBA
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    15 February 2023 4pm (UTC)
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    Montserrat Guillen (University of Barcelona, Spain) Motor insurance with telematics driving data
    Abstract (click to expand) Many insurance companies collect telematics data about drivers’ exposure to traffic (distance driven and type of road), their driving behavior (excess speed, aggressiveness, operating hours) and contextual information (weather conditions, traffic intensity). Actuaries use this information to improve motor insurance ratemaking. Several recent proposals will be presented, mostly using traditional GLM models. In addition, personalized driving risk indicators can also promote driving safety. Illustrations with several real data sets provided by insurance companies will answer questions: (1) How are pay-per-mile insurance schemes be designed? (2) How can near-miss telematics be used to identify risky drivers? (3) What is the power of risk analytics and percentile charts to monitor drivers? Come results on integrating weather conditions will also be discussed.
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    01 March 2023 8am (UTC)
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    Peter Hieber (HEC Lausanne, Switzerland) Designing mutual insurance schemes of heterogeneous risks
    Abstract (click to expand) The tendency of insurance providers to refrain from offering long-term guarantees on investment or mortality risk has shifted attention to mutual risk pooling schemes like (modern) tontines, pooled annuities, or group self-annuitization schemes. There are at least two reasons why it is advantageous to pool policyholders with different risks (for example mortality pools with policyholders of different age and/or health): (1) This allows to increase pool sizes, leading to a reduction in risks. (2) Pooling opposing risks like mortality and morbidity risks helps to further diversify and reduce adverse selection effects. This talk discusses the design of such heterogeneous mutual insurance schemes. It covers aspects of risk sharing as well as risk management and the actuarial fairness of the introduced schemes.

    15 March 2023 3pm (UTC)
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    Margie Rosenberg (University of Wisconsin-Madison, USA) The Importance of Oral Health and Accessibility to Dental Care Services for Medicare Beneficiaries on their General Health Status
    Abstract (click to expand) Oral diseases include dental cavities, gum disease, oral and facial pain, as well as mouth and throat cancers (https://www.who.int/news‐room/fact‐sheets/detail/oral‐health). These problems are cumulative and can result in serious health problems as we age, when these issues are not treated (https://www.nidcr.nih.gov/research/data‐statistics/surgeon‐general). In this work, we focus on Medicare beneficiaries in the US (65+ population) to examine the status of their teeth, along with any barriers to receiving dental care services on their reported general health status. Medicare, the federal health program for those over 65, does not automatically cover beneficiaries for their dental care needs. We use the 2017‐2018 National Health and Nutrition Examination Survey (NHANES) questionnaire. Mobile exam data are available where a licensed dental provider examines the status of each tooth. We create a new dentition status variable that summaries the state of the mouth of the participant into 5 groups: (a) all natural teeth, excluding crowns, (b) those with all teeth positions filled with a combination of natural and restored teeth (crowns, dentures, and implants), (c) those who wear dentures for all teeth positions, (d) those with no natural nor restored teeth (edentulous), and (e) those with less than a full mouth filled with either natural or restored teeth. The first three groups have some form of a tooth in all positions, while the latter two groups are either without any teeth or with fewer than a full mouth of teeth. Any barriers to receiving dental care services reflected the prior 12 months. More than half of the Medicare population have less than a full mouth of teeth, while 15% have complete dentures or are edentulous. Using logistic regression, we find that those with barriers to dental care services have a differential level of associations by dentition status with general health status. Compared to those with all natural teeth, those who have all dentures are significantly more likely to have fair or poor general health status, while the odds ratio for those who are edentulous is smaller in level and not significant. In a sub‐group analysis focusing only on those who are either wearing complete dentures or are edentulous, we find that the barriers to dental care services is not significant factor of fair or poor general health status, yet fair or poor oral health status is a significant factor of fair or poor general health status.

    29 March 2023 8am (UTC)
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    Salvatore Scognamiglio (University of Naples Parthenope, Italy) Accurate and Explainable Mortality Forecasting with the LocalGLMnet
    Abstract (click to expand) Recently, accurate forecasting of mortality rates with deep learning models has been investigated in several papers in the actuarial literature. Most of the models proposed to date are not explainable, making it difficult to communicate the basis on which mortality forecasts have been made. We adapt the LocalGLMnet of Richman and Wüthrich (2023) to produce explainable forecasts of mortality rates using locally connected neural networks, and we show that these can be interpreted as autoregressive time-series models of mortality rates. These forecasts are shown to be highly accurate on the Human Mortality Database and the United States Mortality Database. Finally, we show how regularizing the LocalGLMnet can produce improved forecasts, and that by applying auto-encoders, observations of mortality rates can be denoised to improve forecasts even further.
    26 April 2023 3pm (UTC)
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    María del Carmen Boado-Penas (Heriot-Watt University, UK) Automatic balancing mechanisms for public pension schemes: Past, present and future
    Abstract (click to expand) Public pension systems are usually financed on a pay-as-you-go (PAYG) basis where pensions for retirees are paid by the contributions of the working-age population. With continuous improvements in life expectancy and a decrease in birth rate, pensions are paid over a longer time horizon while the income from contributions become smaller. In this respect, in PAYG schemes, automatic balancing mechanism (ABMs) can be designed to restore the financial sustainability of the system. ABMs can be defined as a set of pre-determined measures established by law to be applied immediately as required according to an indicator that reflects the financial health of the system. Most countries around the world have already legislated and included different types of mechanisms into their pension systems. This work aims to explore different mechanisms that have been set up and analyses their effectiveness. A theoretical construction for the ABM is also proposed and different methods are suggested to guide the system back onto the road to long-term financial stability and at the same time ensure pension adequacy.
    10 May 2023 8am (UTC)
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    Tolulope Fadina (University of Essex, UK)
    24 May 2023 4pm (UTC)
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    Mike Ludkovski (University of California - Santa Barbara, USA) Expressive Mortality Models through Gaussian Process Kernels
    Abstract (click to expand) I will discuss a flexible Gaussian Process (GP) framework for learning the covariance structure of Age- and Year-specific mortality surfaces. Utilizing the additive and multiplicative structure of GP kernels, we design a genetic programming algorithm to search for the most expressive kernel for a given population. Our compositional search builds off the Age-Period-Cohort (APC) paradigm to construct a covariance prior best matching the spatio-temporal dynamics of a mortality dataset. We apply the resulting genetic algorithm (GA) on synthetic case studies to validate the ability of the GA to recover APC structure, and on real-life national-level datasets from the Human Mortality Database. Our machine-learning based analysis provides novel insight into the presence/absence of Cohort effects in different populations, and into the relative smoothness of mortality surfaces along the Age and Year dimensions. Our modelling work is done with the PyTorch libraries in Python and provides an in-depth investigation of employing GA to aid in compositional kernel search for GP surrogates. This is joint work with Jimmy Risk (Cal Poly Pomona) and is based on https://arxiv.org/abs/2305.01728
    07 June 2023 3pm (UTC)
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    Runhuan Feng (University of Illinois at Urbana-Champaign, USA) Distributed Insurance: Tokenization of Risk and Reward Allocation
    Abstract (click to expand) It is fairly common in developed economies that a small set of insurers with large capitalization often account for the majority of their insurance markets. While tight regulations of the insurance industry are well-intended to protect the interests of policyholders and ensure market stability, the legal compliance and capital requirements create prohibitively high barriers that prevent retail investors or small companies from entering the market, further exacerbating the consolidation of the market. The advancement of distributed ledger technology has enabled new models to transfer risks from policyholders to crypto capital market. There has been little to no previous study on the underpinning theory of such new mechanisms. We propose a new theoretical framework for distributed insurance, where risks and rewards can be spread in a large distributed network of retail investors, as opposed to the traditional practice of risk concentrations on insurers. Our findings show that distributed risk sharing can significantly reduce the cost of coverage, improve capital efficiency while meeting the needs for limited liabilities and common investment principles for retail investors.
    13 September 2023 3pm (UTC)
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    Bin Zou (University of Connecticut, USA) Reinsurance Games with Multiple Reinsurers
    Abstract (click to expand) In this talk, I will share our recent progress on reinsurance games under model ambiguity between one representative insurer and multiple reinsurers. We first review a tractable, continuous-time Stackelberg game framework for such a problem in the degenerate case of one reinsurer. We then consider a general case with n reinsurers, all applying the variance premium principle in pricing but with possibly different loadings. The interaction between the insurer and each of the n reinsurers is modelled by a Stackelberg game, and the competition among the reinsurers is resolved by a non-cooperative Nash game. We show that, in equilibrium, the insurer purchases a positive amount of proportional reinsurance from each reinsurer. Last, we conduct a comparison study on the reinsurance structures and find that the insurer always prefers the tree structure to the chain reinstruct. (Based on joint works with Jingyi Cao, Dongchen Li, and Virginia Young.)
    27 September 2023 3pmm (UTC)
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    Ralf Korn (TU Kaiserslautern, Germany) Optimal portfolios with sustainable assets: aspects for life insurers
    Abstract (click to expand) Since August 2022 customers in Germany have to be asked if they are interested in sustainable investment when entering a pension contract. Hence, the provider has to be prepared to offer suitable investment opportunities. Further, the provider has to manage the new risks and chances of those assets in the whole portfolio. We therefore especially look at possible consequences for optimal portfolio decisions of a life insurer and suggest modeling approaches for the evolution of the demand and the sustainability ratings for sustainable assets. We will solve various portfolio problems under sustainability constraints explicitly and suggest further research topics. As a special feature for a life insurer, we particularly look at the role of the actuarial reserve fund and the annual declaration of its return.
    11 October 2023 9am (UTC)
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    Tolulope Fadina (University of Illinois Urbana-Champaign, USA) Optimal reinsurance with multivariate risks and dependence uncertainty
    Abstract (click to expand) In this paper, we study the optimal reinsurance design from the perspective of an insurer with multiple lines of business, where the reinsurance is purchased by the insurer for each line of business respectively. For the risk vector generated by the multiple lines of business, we suppose that the marginal distributions are fixed, but the dependence structure between these risks is unknown. Due to the unknown dependence structure, the optimal strategy is investigated for the worst-case scenario. We consider two types of risk measures: Value-at-Risk (VaR) and Range-Value-at-Risk (RVaR) including Expected Shortfall (ES) as a special case, and general premium principles satisfying certain conditions. To be more practical, the minimization of the total risk is conducted under some budget constraint. For the VaR-based model with only two risks, it turns out that the limited stop-loss reinsurance treaty is optimal for each line of business. For the model with more than two risks, we obtain two types of optimal reinsurance strategies if the marginals have convex or concave distributions on their tail parts by constraining the ceded loss functions to be convex or concave. Moreover, as a special case, the optimal quota-share reinsurance with dependence uncertainty has been studied. Finally, after applying our findings to two risks, some numerical studies have been implemented to obtain the optimal reinsurance policies.
    25 October 2023 3pm (UTC)
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    Peng Shi (University of Wisconsin, USA)

    Cancelled

    08 November 2023 9am (UTC)
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    Corina Constantinescu (University of Liverpool, UK)

    Cancelled

    22 November2023 3pm (UTC)
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    Agni Orfanoudaki (University of Oxford, UK) Algorithmic Insurance
    Abstract (click to expand) As machine learning algorithms get integrated into the decision-making process of companies and organizations, insurance products are being developed to protect their providers from liability risk. Algorithmic liability differs from human liability since it is based on data-driven models compared to multiple heterogeneous decision-makers and its performance is known a priori for a given set of data. Traditional actuarial tools for human liability do not consider these properties, primarily focusing on the distribution of historical claims. We propose, for the first time, a quantitative framework to estimate the risk exposure of insurance contracts for machine-driven liability, introducing the concept of algorithmic insurance. Our work provides ML model developers and insurance providers with a comprehensive risk evaluation approach for this new class of products. Thus, we set the foundations of a niche area of research at the intersection of the literature in operations, risk management, and actuarial science. Specifically, we present an optimization formulation to estimate the risk exposure of a binary classification model given a pre-defined range of premiums. Our approach outlines how properties of the model, such as discrimination performance, interpretability, and generalizability, can influence the insurance contract evaluation. To showcase a practical implementation of the proposed framework, we present a case study of medical malpractice in the context of breast cancer detection. Our analysis focuses on measuring the effect of the model parameters on the expected financial loss and identifying the aspects of algorithmic performance that predominantly affect the risk of the contract.
    Talks in 2022
    Date & Time Speaker Title Misc
    12 January 2022 3pm (UTC)
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    Virginia Young (University of Michigan, USA) Stackelberg Differential Game for Insurance under Model Ambiguity
    Abstract (click to expand) We study a dynamic Stackelberg differential game between a buyer and a seller of insurance policies in a spectrally negative Levy framework, in which both parties are ambiguous about the intensity and severity of insurable losses. Both the buyer and seller aim to maximize their expected wealth, plus a penalty term that reflects ambiguity, over an exogenous random horizon. Under a mean-variance premium principle and a quadratic penalty for ambiguity, we obtain the equilibrium in closed form. Our main results show that the buyer’s robust optimal indemnity is a coinsurance with proportion less than one-half, which increases (resp. decreases) as the buyer (resp. seller) becomes more ambiguity averse. Also we show that the seller’s robust optimal premium rule equals the net premium under the buyer’s optimally distorted probability, which is the buyer’s “best hope,” and it exceeds the actuarially fair premium under the seller’s optimally distorted probability measure so is, thereby, acceptable to the seller
    Host: Pietro Millossovich
    Questions: Jennifer Alonso Garcia
    26 January 2022 3pm (UTC)
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    Emanuela Rosazza Gianin (University of Milano-Bicocca , Italy) Generalized PELVE and applications to risk measures
    Abstract (click to expand) The continuing evolution of insurance and banking regulation has raised interest in the calibration of different risk measures associated with suitable confidence levels. In particular, Li and Wang (2019) have introduced a probability equivalent level (called PELVE) for the replacement of Value at Risk with Conditional Value at Risk. In this talk, we propose a new tool (generalized PELVE, or g-PELVE) that extends PELVE to more general pairs of monotone risk measures. Conditions for the existence and uniqueness of g-PELVE and additional properties for specific families of risk measures are discussed. A study of Generalized Pareto Distributions reveals an interesting correspondence between PELVE and g-PELVE, and explores their relationship with the tail index. An empirical application illustrates the usefulness of (g-)PELVE in characterizing tail behavior not only for individual asset returns, but also for possible portfolio combinations. Based on a joint work with Anna Maria Fiori.
    Host: Andreas Tsanakas
    Questions: Silvana Pesenti
    23 February 2022 3pm (UTC)
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    Julien Trufin (Université Libre de Bruxelles, Belgium) Testing for more positive expectation dependence with application to model comparison and autocalibrated models.
    Abstract (click to expand) Modern data science tools are effective to produce predictions that strongly correlate with responses. Model comparison can therefore be based on the strength of dependence between responses and their predictions. Positive expectation dependence turns out to be attractive in that respect. The present talk proposes an effective testing procedure for this dependence concept and applies it to compare two models. A simulation study is performed to evaluate the performances of the proposed testing procedure. Empirical illustrations using insurance loss data demonstrate the relevance of the approach for model selection in supervised learning. The most positively expectation dependent predictor can then be autocalibrated to obtain its balance-corrected version that appears to be optimal with respect to Bregman, or forecast dominance. Under autocalibration, it is shown that Lorenz curve and concentration curve coincide and that the integral of the concentration curve is equivalent to Gini coefficient.
    Slides

    Host: Silvana Pesenti
    Questions: Munir Hiabu
    09 March 2022 9am (UTC)
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    Fei Huang (University of New South Wales, Australia) Insurance Discrimination and Pricing Fairness
    Abstract (click to expand) On the issue of insurance discrimination, a grey area in regulation has resulted from the growing use of big data analytics by insurance companies – direct discrimination is prohibited, but indirect discrimination using proxies or more complex and opaque algorithms can be tolerated without restrictions. This phenomenon has recently attracted the attention of insurance regulators all over the world, and stricter insurance discrimination regulations are being discussed and considered by regulators. Meanwhile, various fairness criteria and fair machine learning algorithms have been proposed and flourish in the machine learning literature with the rapid growth of artificial intelligence (AI) in the past decade, which mostly focus on classification decisions. In this presentation, I will firstly review social and economic principles that can be used to assess the appropriateness of insurance discrimination. I will then introduce the fairness criteria that are potentially applicable to insurance pricing, match them with different levels of potential and existing anti-discrimination regulations, and implement them into a series of existing and newly proposed anti-discrimination insurance pricing models. Finally, I will compare the outcome of different models from the perspectives of both group fairness and individual fairness and show the cost of fairness.
    Host: Munir Hiabu
    Questions: Andreas Tsanakas
    23 March 2022 3pm (UTC)
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    Alfred Müller (University of Siegen, Germany) Decisions under uncertainty: sufficient conditions for almost stochastic dominance
    Abstract (click to expand) Decision making under risk in actuarial sciences as well as in other disciplines involves a ranking of distributions, which is typically based on a method for assigning a real number to a distribution using a risk measure, a premium principle or a context of expected utility. As it is typically difficult to assess a concrete risk measure or utility function it is a well established idea to use stochastic dominance rules in form of stochastic orders to compare distributions. However, it is often equally difficult to completely specify a distribution. Therefore it is an interesting question whether one can derive unambiguous decisions under partial knowledge of the distributions. In this talk we in particular address this question under the condition that we only know the mean and variance of the involved distributions or that we know the marginal distributions but not the copulas in a multivariate context. Under such assumptions we derive sufficient conditions for concepts of almost stochastic dominance that are based on restrictions on marginal utilities. The talk is based on joint work with Marco Scarsini, Ilia Tsetlin and Robert L. Winkler
    Host: Silvana Pesenti
    Questions: Ruodu Wang
    6 April 2022 Spring Break
    20 April 2022 12pm (UTC)
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    Christian Furrer (University of Copenhagen, Denmark) Change of measure techniques for scaled insurance cash flows
    Abstract (click to expand) Incidental policyholder behavior, including free policy conversion and stochastic retirement, may have a significant impact on the market value of a life insurance contract; consequently, models should account for this. However, the inclusion of incidental policyholder behavior typically leads to duration effects and thus an increase in computational complexity. In this talk, I show how change of measure techniques can be used to conveniently deal with this added layer of complication.
    Host: Munir Hiabu
    Questions: Jennifer Alonso Garcia
    04 May 2022 8am (UTC)
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    Annamaria Olivieri (University of Parma, Italy) Flexible annuity designs meeting individuals’ longevity risk appetite (or unawareness)
    Abstract (click to expand) Despite the growing need for individuals to protect themselves from the longevity risk to which their assets will be exposed after retirement, the demand for products offering longevity guarantees, namely annuities, remains low. Possible reasons include the cost of guarantees and the rigidity of the traditional annuity design, which implies an irreversible decision at issue. This contrasts with the perspective of individuals who, because of their risk appetite or unawareness, seem to prefer to avoid non-revisable decisions, at least in the early stages of their post-retirement life, and to retain their longevity risk up to some higher age. Flexibility in the annuity design could, at least partially, meet the prevailing individuals’ attitude. Flexibility can be introduced in different ways. We focus on two solutions. First, the guarantees can be relaxed, and the related costs can be reduced, by allowing the benefit amount to fluctuate (up or down) according to a given mortality/longevity experience. Second, instead of an upfront loading at issue, periodic fees could be charged, as they are more suitable to support a revision of the arrangement after issue. While the literature includes already several contributions on mortality/longevity-linked benefits, a pricing structure based on periodic fees has received little attention so far. We develop a discussion in this respect, considering mortality/longevity-linked annuities
    Host: Andrés Villegas
    Questions: Jennifer Alonso Garcia
    18 May 2022 8am (UTC)
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    Johanna Ziegel (University of Bern, Switzerland) Distributional (Single) Index Models
    Abstract (click to expand) A Distributional (Single) Index Model (DIM) is a semiparametric model for distributional regression, that is, estimation of conditional distributions given covariates. The method is a combination of classical single- index models for the estimation of the conditional mean of a response given covariates, and isotonic distributional regression. The model for the index is parametric, whereas the conditional distributions are estimated nonparametrically under a stochastic ordering constraint. We show consistency of our estimators and apply them to a highly challenging dataset on the length of stay (LoS) of patients in intensive care units. We use the model to provide skillful and calibrated probabilistic predictions for the LoS of individual patients, which outperform the available methods in the literature.
    Host: Andreas Tsanakas
    Questions: Munir Hiabu
    01 June 2022 8am (UTC)
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    Benjamin Avanzi (The University of Melbourne, Australia) Ensemble distributional forecasting for insurance loss reserving
    Abstract (click to expand) Loss reserving generally focuses on identifying a single model that can generate superior predictive performance. However, different loss reserving models specialise in capturing different aspects of loss data. This is recognised in practice in the sense that results from different models are often considered, and sometimes combined. For instance, actuaries may take a weighted average of the prediction outcomes from various loss reserving models, often based on subjective assessments. In this paper, we propose a framework to objectively combine (i.e. ensemble) multiple stochastic loss reserving models such that the strengths offered by different models can be utilised effectively. Criteria of choice consider the full distributional properties of the ensemble. A notable innovation of our framework is that it is tailored for the features inherent to reserving data. These include, for instance, accident, development, calendar, and claim maturity effects. Crucially, the relative importance and scarcity of data across accident periods renders the problem distinct from the traditional ensembling techniques in statistical learning. Our ensemble reserving framework is illustrated with a complex synthetic dataset. In the results, the optimised ensemble outperforms both (i) traditional model selection strategies, and (ii) an equally weighted ensemble. In particular, the improvement occurs not only with central estimates but also relevant quantiles, such as the 75th percentile of reserves (typically of interest to both insurers and regulators). This is joint work with Yanfeng Li, Bernard Wong, and Alan Xian
    Host: Andrés Villegas
    Questions: Munir Hiabu
    21 September 2022 8am (UTC)
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    Jim Guszcza (Deloitte, USA) Professionalizing Artificial Intelligence: Lessons from Actuarial Science
    Abstract (click to expand) Artificial Intelligence is often characterized in terms of “solving intelligence” or building machines that outperform humans at most economically meaningful work. But for scientific, economic, as well as societal reasons, this paradigm is likely to give way to a more design-focused paradigm of creating human-machine hybrid intelligence systems. This talk will sketch the Hybrid Intelligence paradigm, and discuss various ways in which the needed field of Hybrid Intelligence engineering must adopt traits characteristic of the actuarial profession: a respect for data limitations, an acknowledgment of the need to integrate algorithmic indications with local knowledge and informed judgment; and an ethos of ethical behavior and public service. The discussion will be motivated by examples from insurance and other domains.
    Host: Pietro Millossovich
    Questions: Andreas Tsanakas
    Slides
    05 October 2022 3pm (UTC)
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    Sheldon Lin (University of Toronto, Canada) An Effective Simulation Scheme for the Valuation of Large Heterogeneous Insurance Portfolios
    Abstract (click to expand) Insurance policies are mostly individual specific, as policyholders possess different risk characteristics and choose different policy options to meet their needs. Thus, the probability distributions that underlie the insurance claims are policy specific and complex, as opposed to the common parametric distributions. As a result, calculating the quantities of interest (e.g. premiums, liabilities, etc.) can only be done via stochastic simulations individually. Moreover, in reality an insurance portfolio contains hundreds of thousands of policies. In other words, we are dealing with a very large and highly heterogeneous insurance portfolio. To obtain any quantity of interest via simulation across the entire portfolio is extremely time consuming and is very often prohibitive. In this talk, we propose an effective simulation scheme that only involves the simulation of a very small number of the policies in the portfolio. The first step is to select this small set of policies using a population sampling technique, i.e. the Delta method, so that the entire portfolio is well represented by the selected policies. A tailor-made simulation algorithm is applied to those representative policies. We then identify a policy specific quantity or summary statistics that well describe the information from a policy (policy attributes and claims) and introduce a model (surrogate model) that links the quantity/statistics to the quantity of interest we intend to calculate. The surrogate model is estimated using the representative policies and is then used for extrapolation (to calculate the quantity for the rest of the policies). We illustrate this simulation scheme with two very different examples. One is the valuation and hedging of a variable annuity (VA) portfolio and the other is on the calculation of the Bayesian premiums of an auto insurance portfolio.
    Host:Jennifer Alonso Garcia
    Questions: Silvana Pesenti
    19 October 2022 8am (UTC)
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    Anne Balter (Tilburg University, The Netherlands) Robust Decisions for Heterogeneous Agents via Certainty Equivalents
    Abstract (click to expand) We study the problem of a planner who resolves risk-return trade-offs - like financial investment decisions - on behalf of a collective of agents with heterogeneous risk preferences. The planner's objective is a two-stage utility functional where an outer utility function is applied to the distribution of the agents' certainty equivalents from a given decision. Assuming lognormal risks and heterogeneous power utility preferences for the agents, we characterize optimal behavior in a setting where the planner can let each agent choose between different options from a fixed menu of possible decisions, leading to a grouping of the agents by risk preferences. These optimal decision menus are derived first for the case where the planner knows the distribution of preferences exactly and then for a case where he faces uncertainty about this distribution, only having access to upper and lower bounds on agents' relative risk aversion. Finally, we provide tight bounds on the welfare loss from offering a finite menu of choices rather than fully personalized decisions.
    Host: Munir Hiabu
    Questions: Jennifer Alonso Garcia
    02 November 2022 4pm (UTC)
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    Munir Hiabu (University of Copenhagen, Denmark) Planted Machine Learning: Letting performance and interpretability go hand in hand
    Abstract (click to expand) The goal of Planted Machine Learning is to discover and learn low dimensional structures that can get more complex along a planted path. I will introduce Random Planted Forest – an algorithm we have recently developed that seems to be competitive with state-of-the-art machine learning predictors with respect to accuracy while having favourable interpretability properties. In the second part of the talk, we will contrast local explanations like SHAP values to the interpretation of global structures and by doing so touching topics on causality, fairness and variable importance.
    Slides

    Host: Silvana Pesenti
    Questions: Pietro Millossovich
    Autumn Break
    30 November 2022 4pm (UTC)
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    Brian Hartman (Brigham Young University, USA) A Multivariate Spatiotemporal Model for County-Level Mortality Data in the Contiguous United States
    Abstract (click to expand) Using a number of modern predictive modeling methods, we seek to understand the factors that drive mortality in the contiguous United States. The mortality data we use is indexed by county and year as well as grouped into 18 different age bins. We propose a model that adds two important contributions to existing mortality studies. First, instead of building mortality models separately by age or treating age as a fixed covariate, we treat age as a random effect. This is an improvement over previous models because it allows the model in one age group to borrow strength and information from other age groups that are nearby. The result is a multivariate spatiotemporal model and is estimated using Integrated Nested Laplace Approximations (INLA). Second, we utilize Gaussian Processes to create nonlinear covariate effects for predictors such as unemployment rate, race, and education level. This allows for a more flexible relationship to be modeled between mortality and these important predictors. Understanding that the United States is expansive and diverse, we also allow for many of these effects to vary by location. The amount of flexibility of our model in how predictors relate to mortality has not been used in previous mortality studies and will result in a more accurate model and a more complete understanding of the factors that drive mortality. Both the multivariate nature of the model as well as the non-linear predictors that have an interaction with space will advance the study of mortality beyond what has been done previously and will allow us to better examine the often complicated relationships between the predictors and mortality in different regions.
    Slides

    Host: Jennifer Alonso Garcia
    Questions: Munir Hiabu
    14 Decmber 2022 9am (UTC)
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    Valeria Bignozzi (University of Milano-Bicocca, Italy) Inter-order relations between moments of a Student t distribution, with an application to L_p-quantiles
    Abstract (click to expand) In this work we focus on a class of risk measures denoted L_p-quantiles, which represent a class of generalized quantiles defined through an asymmetric p-power loss function. In particular, we show that for a Student t distribution with n degrees of freedom, the L_{n−j+1}-quantile and the L_j -quantile coincide at any confidence level τ in (0, 1). This result is based on inter-order formulas for partial and complete moments of the Student t distribution. We show how the partial moment of order n − j about any real value m can be expressed in terms of the partial moment of order j − 1 for j in {1, . . . , n}. Closed form expressions for the complete moments are also established.
    Host: Andrés Villegas
    Questions: Pietro Millossovich
    Talks in 2021
    Date & Time Speaker Title Misc
    13 January 2021 4pm (UTC, London)
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    Marius Hofert (University of Waterloo, Canada) Statistical methods for understanding and decoding evolutionary processes
    Abstract (click to expand) Two of my major research interests are statistical methods for (a) understanding genetic diversity within populations, and (b) decoding mutational processes in cancer evolution. In this talk I will describe the core probability models in these two areas of molecular evolution. In particular I plan to emphasize recent developments and challenges that could serve as foundations for future collaborations.
    Slides
    27 January 2021 4pm (UTC, London)
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    Carole Bernard (Grenoble Ecole of Management, France) Optimal collective financial decision making
    Abstract (click to expand) In this talk, we will discuss optimal portfolio choice for an agent (e.g., a social planner) who aims to maximize a multivariate objective such as an expected multivariate utility. We first relate this problem to a problem of cost-efficient allocation, which consists in finding the cheapest multidimensional payoff achieving a given joint distribution. We then characterize the optimal portfolio in a general setting, provide a numerical procedure to obtain an optimal allocation, and derive explicit expressions in the Gaussian case. We discuss desired properties for the multivariate objective function in order to ensure that optimal portfolios are not comonotonic. Important potential applications, such as reducing systemic risk or estimating the cost of ``constrained diversification," are also examined. This is a joint work with Luca De Gennaro and Steven Vanduffel.
    10 February 2021 4pm (UTC, London)
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    Melina Mailhot (Concordia University, Canada)
    Frédéric Godin (Concordia University, Canada)
    Geometric risk measures for risk management and semi-parametric estimation of multivariate extreme expectiles
    Abstract (click to expand) Using the geometric representation of risk measures does not provide as straightforward interpretation of how risky a position is, compared to using distribution-based risk measures. However, in this presentation, we will see how they can bring insightful information and help assessing multivariate risks. Moreover, special attention will be brought to providing a semi-parametric estimator for multivariate extreme expectiles. Illustrations using simulated and real data will be provided.
    24 February 2021 9am (UTC, London)
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    An Chen (Ulm University, Germany) Linking risk management under expected shortfall to loss-averse behavior (joint work with Thai Nguyen)
    Abstract (click to expand) We introduce and solve an optimal asset allocation problem under a weighted expected shortfall (WES) constraint, which contains the risk management problem under an expected shortfall constraint of Basak and Shapiro (2001) as a special case. Furthermore, we link our risk management problem under the WES constraint with an optimal asset allocation with a multiple-reference-based preference (MRBP) and find that the optimal wealth with MRBP owns the same form as the optimal solution under the WES constraint. For the degenerate case with a fixed reference level, we are able to determine the critical maximal allowed expected shortfall constraint as a function of the loss aversion parameters to achieve equivalence. It is interesting to observe that, while no equivalence can be in general obtained between the WES and the MRBP solution, the optimal terminal wealth of the WES can be made to coincide with the MRBP terminal wealth in the most favorable and in the worst market states. In addition, we carry out a general equilibrium analysis in the presence of a WES/MRBP risk manager.
    10 March 2021 8am (UTC, London)
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    Mario Giuricich (PwC, South Africa) TBA
    Abstract (click to expand) TBA
    10 March 2021 2pm (UTC, London)
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    Silvana Pesenti (University of Toronto, Canada) Reverse Sensitivity Analysis for Risk Modelling
    Abstract (click to expand) We consider the problem where a modeller conducts sensitivity analysis of a model consisting of random input factors, a corresponding random output of interest, and a baseline probability measure. The modeller seeks to understand how the model (the distribution of the input factors as well as the output) changes under a stress on the output's distribution. Specifically, for a stress on the output random variable, we derive the unique stressed distribution of the output that is closest in the Wasserstein distance to the baseline output's distribution and satisfies the stress. We further derive the stressed model, including the stressed distribution of the inputs, which can be calculated in a numerically efficient way from a set of baseline Monte Carlo samples. The proposed reverse sensitivity analysis framework is model-free and allows for stresses on the output such as (i) the mean and variance, (ii) any distortion risk measure including the Value-at-Risk and Expected-Shortfall, and (iii) expected utility type constraints, thus making the reverse sensitivity analysis framework suitable for risk models.
    24 March 2021 4pm (UTC, London)
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    Robert Erhardt (Wake Forest University, USA) The Changing Spatial Dependence in Flood Risk: A Loss Occurrence Study in the United States
    Abstract (click to expand) Flood represents one of the costliest and most disruptive natural disasters in the United States, and the economic losses from flooding are trending upward. While this trend is known to be driven primarily by an increasing population and increasing wealth exposure, climate change is also impacting flood risk in more subtle ways. We merge data on economic flood losses, historical climate, census population, and geological characteristics to explore trends in the spatial dependence of economic flood loss occurrence across 292 hydrobasins from 1979-2018 in the United States. We then fit an autologistic statistical model for flood loss occurrence, control for known covariates, and quantify climate drivers of flood risk occurrence. We show empirically that measures of spatial clustering and dependence have been decreasing over the study period, and through a simulation study with our statistical model we document how these trends are caused in part by a changing climate, and are expected to continue. This work is joint with Mathieu Boudreault at UQAM, David Carozza at UQAM, and Kejia Yu at WFU.
    07 April 2021 Spring Break
    21 April 2021 9am (UTC)
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    Rui Zhou (University of Melbourne, Australia) The Role of Longevity Annuities in Different Socioeconomic Classes: A Canadian Case Study
    Abstract (click to expand) Longevity annuity is a deferred annuity where payments start very late in life, i.e. well after the normal retirement age, 65. By transferring the risk of outliving retirement savings at high ages to annuity providers, longevity annuity provides annuitants with enhanced later-life financial security. In this paper, we examine the impact of longevity annuity provision on retirement income planning based on Canadian tax rules and the Canadian retirement system. A dynamic life cycle framework is developed to study welfare increase and consumption pattern changes resulting from the provision of longevity annuities to Canadian retirees. To determine the optimal choices in the life cycle model, we propose a modified general endogenous grid method (GEGM) which addresses the non-differentiability problem arising from realistic tax rules and a realistic retirement system. This life cycle framework and modified GEGM are further applied to explore how individuals in different social classes respond to the access to longevity annuities.
    05 May 2021 12noon (UTC)
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    George Tzougas (London School of Economics, UK) Neural Network Embedding of the Negative Binomial Regression Model for Claim Frequencies Joint work with Ziyi Li
    Abstract (click to expand) The aim of this paper is to embed the overdispersed Negative Binomial regression model for claim counts into a neural network architecture following the Combined Actuarial Neural Network approach (CANN) approach of Wuthrich and Mertz (2019). The implementation of the blended model is illustrated by a real data application which involves fitting French motor third-party liability (MTPL) insurance data. We demonstrate that the neural net boosting of the Negative Binomial regression model allows us to explore missing interactions of nonmultiplicative type that cannot be captured by the Negative Binomial Regression model.
    19 May 2021 12noon (UTC)
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    María Óskarsdóttir (Reykjavik University, Iceland) Social network analytics for supervised fraud detection in insurance and beyond
    Abstract (click to expand) Fraud occurs in the insurance industry when policyholders file claims that are exaggerated or based on intentional damage. In organized crime, such as fraud, social relations are important as they provide access to co-offenders, profitable opportunities and invigorate trust. In this talk, we present a novel approach to detect fraudulent insurance claims using bipartite networks of claims and involved parties that represent the social structures of collaborating fraudsters. We compute fraud scores based on influence from the fraudulent claims in the network and extract features using the fraud scores and the claims’ neighborhood. We combine these network features with the intrinsic features in a supervised model with fraud as the target variable. The high performance of the model with all features indicates that the network features provide valuable information which complements the information contributed by the intrinsic features. The resulting model can be used to flag suspicious claims. We also discuss applications of our proposed method in other areas, such as credit scoring.
    02 June 2021 4pm (UTC)
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    Natalia Nolde (University of British Columbia, Canada) An extreme value approach to CoVaR estimation
    Abstract (click to expand) The global financial crisis of 2007-2009 highlighted the crucial role systemic risk plays in ensuring stability of financial markets. Accurate assessment of systemic risk would enable regulators to introduce suitable policies to mitigate the risk as well as allow individual institutions to monitor their vulnerability to market movements. One popular measure of systemic risk is CoVaR. We propose a methodology to estimate CoVaR semi-parametrically within the classical framework of multivariate extreme value theory. According to its definition, CoVaR can be viewed as a high quantile of a conditional distribution where the conditioning event corresponds to large losses of a given institution. We relate this conditional distribution to the tail dependence function. In the estimation procedure, we combine parametric modelling of the tail dependence function to address the issue of data sparsity in the joint tail regions and semi-parametric univariate high quantile estimation techniques. We prove consistency of the estimator, and illustrate its performance via simulation studies and a real data example. This is a joint work with Chen Zhou (Erasmus University) and Menglin Zhou (University of British Columbia).
    18 August 2021 8am (UTC)
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    Hamza Hanbali (Monash University, Australia) Detection of insurance price cycles using neural networks
    Abstract (click to expand) The underwriting cycle refers to the repetitive patterns of ups and downs in premium rates of property-liability insurance. Since the U.S. liability crisis of the 1980's, the underwriting cycle has become a central topic in the research agenda of the insurance economics literature. Virtually all existing studies have used accounting data to study cycles in loss ratios, which is a measure of profitability, and not a measure of price. This is because insurance companies typically do not report price and quantity separately. Although the cyclical patterns in profitability are suspected to be inherited from those in prices, there is, to the best of knowledge, no evidence that premium rates exhibit a cyclical behavior. Further, recent studies argue that insurance cycles do not exist at all. They question the relevance of AR(2) processes, which is the usual methodology used to identify cycles in profitability, and argue that they can lead to the detection of spurious cycles in what could simply be random walks. The present work addresses two related questions. Namely, do insurance prices exhibit a cyclical behavior? and in case they do, how can these patterns be detected in a reliable way? Based on a simulation study, the paper investigates the performance of difference cycle detection methods, and finds that a hybrid neural network architecture combining both convolutional and recurrent layers achieves a high accuracy of 98.06%. This architecture is then applied to market premium rates from the Brazilian automobile insurance industry for a large number of different risk profiles. The results provide strong evidence that premiums for most risk profiles exhibit a cyclical behavior.
    01 September 2021 3pm (UTC)
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    Nora Muler (Universidad Torcuato Di Tella, Argentina) Optimal dividend payment under constraints
    Abstract (click to expand) In this talk we will discuss the problem of optimal dividend rate payment (with a giving ceiling on dividend rates) for a surplus process under the additional constraint of drawdown; that is dividend rates should not decrease more than a given fraction b∈(0,1) of the historical peak. We also address the case in which b=1, this corresponds to a ratcheting constraint on dividends (i.e. the dividend payment rate can never decrease). We maximize the expectation of the discounted cumulative dividend payment up to ruin time. Using the Dynamic Programming Principle, we can show that the optimal value function is the unique viscosity solution of the corresponding two dimensional Hamilton-Jacobi-Bellman equation. In the case that the surplus follows a Brownian motion and the dividend payment rates have a ratcheting constraint, we find the value function corresponding to one-curve strategies (that are the natural extension to two dimensions of the threshold strategies). In these type of strategies, the curve partitions the state space in two regions: one in which the dividends are paid at the current dividend rate and the other in which the dividend rates increases. Afterwards,we use calculus of variations in order to obtain the best value function among these type of curve strategies. The optimal curve is obtained as the unique solution of an ODE. In the case that the dividend payment rate has a drawdown constraint we find value functions corresponding to two-curve strategies. In these type of strategies, the two curves partition the state space in three regions:a region in which dividends are paid at b times the historical peak rate (minimum rate allowed), a region (that is located in between the two curves) in which dividend rates are paid at the historical peak and a region in which dividend rates increases above the historical peak. One more time, we use calculus of variations to obtain the best strategy but this time among these two-curves strategies. These optimal two curves are obtained as the unique solution of a system of ODE's. We present numerical examples and show how the drawdown case, as b decreases from 1 to 0, approach the (usual) one dimensional problem without constraints on dividend rates (which corresponds to b=0). Additionally, we study the limit problem when the ceiling on dividend rates go to infinity. This is a joint work with Hansjoerg Albrecher and Pablo Azcue.
    15 September 2021 12pm (UTC)
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    Caroline Hillairet (ENSAE-Paris, FRANCE) Propagation of cyber incidents in an insurance portfolio
    Abstract (click to expand) In this talk, we propose a general framework to design accumulation scenarios that can be used to anticipate the impact of a massive cyber attack on an insurance portfolio. The aim is also to emphasize the role of countermeasures in stopping the spread of the attack over the portfolio, and to quantify the benefits of implementing such strategies of response. Our approach consists of separating the global dynamic of the cyber event (that can be described through compartmental epidemiological models), the effect on the portfolio, and the response strategy. This general framework allows us to obtain Gaussian approximations for the corresponding processes, and sharp confidence bounds for the losses. A detailed simulation study, which mimics the effects of a Wannacry scenario, illustrates the practical implementation of the method. Joint work with Olivier Lopez. https://hal.archives-ouvertes.fr/hal-02564462v2
    Slides
    29 September 2021 3pm (UTC)
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    Daniel Bauer (University of Wisconsin–Madison, USA) The Marginal Cost of Risk and Capital Allocation in a Property and Casualty Insurance Company (with Qiheng Guo and George H. Zanjani)
    Abstract (click to expand) We develop a multi-period profit maximization model for a property and casualty (P&C) insurance company and use it for determining the marginal cost of risk for different lines of business and resulting economic capital allocations. In contrast to previous literature, our model features a loss structure that matches the characteristics of a P&C company, comprising so-called “short-tailed” and “long-tailed” business lines with different expected settlement terms. As one key contribution, our theoretical and numerical results show that lines with different terms are assessed differently, depending on the company’s financial situation. Paper link: https://danielbaueracademic.files.wordpress.com/2021/09/guobauerzanjani_pandcallocation.pdf
    13 October 2021 9am (UTC)
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    Filip Lindskog (Stockholm University, Sweden) Multiple-prior valuation of cash flows subject to capital requirements
    Abstract (click to expand) We study market-consistent valuation of liability cash flows motivated by current regulatory frameworks for the insurance industry. Building on the theory on multiple-prior optimal stopping we propose a valuation functional with sound economic properties that applies to any liability cash flow. Whereas a replicable cash flow is assigned the market value of the replicating portfolio, a cash flow that is not fully replicable is assigned a value which is the sum of the market value of a replicating portfolio and a positive margin. The margin is a direct consequence of considering a hypothetical transfer of the liability cash flow from an insurance company to an empty corporate entity set up with the sole purpose to manage the liability run-off, subject to repeated capital requirements, and considering the valuation of this entity from the owner's perspective taking model uncertainty into account. Aiming for applicability, we consider a detailed insurance application and explain how the optimisation problems over sets of probability measures can be cast as simpler optimisation problems over parameter sets corresponding to parameterised density processes appearing in applications. Joint work with Hampus Engsner and Julie Thøgersen
    27 October 2021 8am (UTC)
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    (There was a typo in the calendar entries for the end-time. This is fixed now.)
    Wenjun Zhu (Nanyang Technological University, Singapore) Duration-Hedging Trades, Return Momentum and Reversal
    Abstract (click to expand) We study the duration-hedging trades of duration-sensitive strategic investors, i.e., pensions and life insurers. We use longevity shocks to identify their duration-hedging trades. Longevity shocks affect these investors’ liability duration and induce them to adjust their asset duration. When longevity shocks are low (high), they buy more short- (long-) duration stocks and sell more long- (short-) duration stocks. Because prior winners (losers) have shorter (longer) duration, they behave like momentum (contrarian) traders when longevity shocks are low (high). We further verify this channel using capital flows and cross-state longevity variations.
    10 November 2021 4pm (UTC)
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    Anne MacKay (UQAM Montréal, Canada) VIX-linked fee analysis via continuous-time Markov chain methods
    Abstract (click to expand) We consider variable annuity (VA) contracts in which the insurance fee is linked to the VIX index and study the impact of the fee structure on the optimal surrender strategy. Approximating the VA account value and the volatility processes by a two-layer continuous-time Markov chain allows us to work with various VIX-linked fee structures and a wide class of stochastic volatility models, thus generalizing the framework of Cui et al. (2017). We discuss a simple condition under which early surrenders are suboptimal, and present a fast algorithm to approximate the value of the VA contract when this condition is not satisfied. Extensive numerical examples are carried out to illustrate the impact of the fee structure on optimal policyholder behaviour.
    24 November 2021 12pm (UTC)
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    Luitgard Veraart (London School of Economics, UK) When does portfolio compression reduce systemic risk?
    Abstract (click to expand) We analyse the consequences of portfolio compression on systemic risk. Portfolio compression is a post-trading netting mechanism that reduces gross positions while keeping net positions unchanged and it is part of the financial legislation in the US (Dodd-Frank Act) and in Europe (European Market Infrastructure Regulation). We derive necessary structural conditions for portfolio compression to be harmful and discuss policy implications. In particular, we show that the potential danger of portfolio compression comes from defaults of firms that conduct portfolio compression. If no defaults occur among those firms that engage in compression, then portfolio compression always reduces systemic risk.
    08 December 2021 4pm (UTC)
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    Shengchao Zhuang (University of Nebraska-Lincoln, USA) S-shaped narrow framing, skewness and the demand for insurance
    Abstract (click to expand) The existing literature in insurance economics has shown that narrow framing can explain why people buy too little insurance compared to what standard theory predicts. However, there is also ample evidence suggesting people sometimes buy too much insurance. In this paper, we assume S-shaped narrow framing, i.e., the local utility function for evaluating the net insurance payoff is convex in the loss domain but concave in the gain domain, and show that it can reconcile with both insurance puzzles simultaneously. Especially, we show the policyholder under S-shaped narrow framing is more likely to underinsure more negatively skewed risks of loss but to overinsure less negatively skewed risks of loss when only coinsurance is offered. We further characterize the optimal insurance scheme under S-shaped narrow framing while incentive compatibility is satisfied. It contains a straight deductible when the net insurance payoff is negative but partial insurance when the net insurance payoff is positive. This is a joint work with Jiakun Zheng and Yichun Chi.
    Talks in 2020
    Date & Time Speaker Title Misc
    22 April 2020 9am (GMT+1, London)
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    Mario Wuethrich (ETH, Zurich) From Generalized Linear Models to Neural Networks, and Back
    Abstract (click to expand)

    We present how to enhance classical generalized linear models by neural network features. On the way there, we highlight the traps and pitfalls that need to be avoided to get good statistical models. This includes the non-uniqueness of sufficiently good regression models, the balance property, and representation learning, which brings us back to the concept of the good old generalized linear models.

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    06 May 2020 1am (GMT+1, London)
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    Katja Hanewald (UNSW, Sydney) Long-term care insurance financing using home equity release: Evidence from an experimental study
    Abstract (click to expand)

    We explore new mechanisms to fund long-term care using housing wealth. We conduct and analyze an online experimental survey fielded to a representative sample of 1,200 Chinese homeowners aged 45-64 to assess the potential demand for new financial products that allow individuals to access their housing wealth to buy long-term care insurance. We find that the stated demand for long-term care insurance increases when individuals can use housing wealth in addition to savings to purchase long-term care insurance. Individuals prefer to access housing wealth through a reverse mortgage loan rather than home reversion (a partial sale of housing wealth). Our results inform current policy reforms in China which aim at developing the private market for health and long-term care insurance products.

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    20 May 2020 1pm (GMT+1, London)
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    Moshe Milevsky (York University, Toronto) Is Covid-19 a parallel shift of the term structure of mortality? Implications for annuity pricing
    Abstract (click to expand)

    This presentation – which admittedly is rather speculative – examines the financial implications of a sudden shock to mortality on the pricing of pension & life annuities. Now, a textbook approach would suggest that holding interest rates constant, an increase in mortality reduces the discounted value of longevity-contingent claims. Stated simply, life insurance gets expensive and annuities become cheaper. However, if the shock to mortality actually weeds-out the frail and merely advances imminent deaths, then survivors will find that (counter-intuitively) annuities are suddenly dearer. Add plummeting interest rates and depressed equity markets to the mix and soon-to-be retirees might be facing an exceedingly higher "cost of retirement" post 2020. Technically speaking these matters tie into so-called compensation laws and the convergence of the term structure of (stochastic) mortality at very advanced ages. These matters also relate to the distinction between chronological age versus biological age and the relevant clock for measuring any shocks to mortality. In sum, this (conjectural) presentation speculates on how to “think” about covid-19 from the perspective of retirement income planning. One thing is for certain, the first-order independence between shocks to mortality (i.e. the insurance measure) and the economy (i.e. the financial measure) can no longer be assumed, even for textbook actuarial models.

    Slides
    03 June 2020 4pm (GMT+1, London)
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    Ruodu Wang (University of Waterloo, Waterloo) PELVE: Probability Equivalent Level of VaR and ES
    Abstract (click to expand)

    Inspired by the recent transition from the 99% Value-at-Risk (VaR) to the 97.5% Expected Shortfall (ES) for internal market risk models in the Fundamental Review of the Trading Book (FRTB), we introduce a new distributional index, the probability equivalence level of VaR and ES (PELVE), which identifies the balancing point for the equivalence between VaR and ES. PELVE enjoys many desirable theoretical properties and it distinguishes heavy-tailed distributions from light-tailed ones via a threshold 2.72. Applying PELVE to financial asset and portfolio data leads to interesting observations that are not captured by VaR or ES alone. For instance, empirical PELVE exhibit unprecedented jumps during the COVID-19 period, which is not the case for VaR or ES. Moreover, the transition from VaR to ES in the FRTB yields an increase in risk capital for single-asset portfolios, but for well-diversified portfolios, the capital requirement remains almost unchanged. This leads to both a theoretical justification and an empirical evidence for that the use of ES rewards portfolio diversification more than the use of VaR. The talk is based on joint work with Hengxin Li (University of California, Berkeley).

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    17 June 2020 1pm (GMT+1, London)
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    Katrien Antonio (KU Leuven, Belgium) Claims reserving in non-life insurance: old and new adventures
    Abstract (click to expand)

    Claims reserving deals with the prediction of the remaining development of reported, open claims (the reported but not settled reserve) and unreported claims (the incurred but not reported reserve). Micro-level or granular reserving approaches the reserving problem by using granular, detailed data on the development of individual claims. In this talk we briefly present recent work on modelling the number of incurred but not reported (ibnr) claims. We continue with presenting a modular, yet interpretable framework for including claim- and policy-specific covariates in reserving models for reported but not settled (rbns) claims. In this framework, reserving models are tailed to the portfolio at hand by adding building blocks for the events (e.g. settlement, payment, …) registered over the lifetime of a claim. This talk concentrates on a specific model structure with three events describing the development of a claim : the time to settlement, the number of payments and the size of each payment. We propose model selection techniques for predictive models adapted for censored data to select the relevant covariates in these models and demonstrate how the selected covariates determine the granularity of our reserving model. We illustrate the method with case studies on real life insurance data sets. These case studies provide new insights in the covariates driving the development of claims and demonstrate the accuracy and robustness of the reserving methodology over time. The talk is based on joint work with Jonas Crevecoeur, Roel Verbelen and Gerda Claeskens.

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    01 July 2020 9am (GMT+1, London)
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    Han Lin Shang (Macquarie University, Australia) Coherent forecasting age distribution of death counts for multiple populations
    Abstract (click to expand)

    We consider a compositional data analysis approach to forecasting the age distribution of death counts for multiple populations. When modelling the age distribution of death counts for multiple populations, we need to consider at least two features: (1) how to incorporate any possible correlation among multiple populations to potentially improve point and interval forecast accuracy through multi-population joint modelling; (2) how to forecast multiple age distributions of death counts so that the forecasts are non-negative and have a constrained integral. To address these two issues, we introduce an extension of the compositional data analysis of Kokoszka, Miao, Petersen and Shang (2019, International Journal of Forecasting). Using the age-specific period life table death counts in Australia from 1921 to 2016 obtained from the Human Mortality Database (2020), we investigate 1-step-ahead to 20-step-ahead point and interval forecast accuracies of our models and make recommendations. The improved forecast accuracy of period life table death counts is of great interest to demographers for estimating survival probabilities and life expectancy, and to actuaries for determining temporary annuity prices for various ages and maturities.

    Slides
    15 July 2020 1pm (GMT+1, London)
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    Rodrigo Targino (Getulio Vargas Foundation, Brazil) Avoiding zero probability events when computing Value at Risk contributions
    Abstract (click to expand)

    In this presentation I will discuss the process of risk allocation for a generic multivariate model when the risk measure is chosen as the Value-at-Risk (VaR). I will show how to recast the traditional Euler contributions from an expectation conditional to an event of zero probability to a ratio of conditional expectations, where both the numerator and the denominator's conditioning events have positive probability. For several different models we show empirically that the estimator using this novel representation has no perceivable bias and variance smaller than a standard estimator used in practice. Reference: https://arxiv.org/abs/2004.13235

    Slides
    29 July 2020

    Summer break
    12 August 2020 9am (GMT+1, London)
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    KC Cheung (The University of Hong Kong, Hong Kong) Asymptotic sub/super-additivity of Value-at-Risk under extreme-value copulas and Archimedean copulas
    Abstract (click to expand)

    In this talk, we study the asymptotic sub/super-additivity of Value-at-Risk under extreme-value copulas, when the marginal risks of the portfolio are identically distributed, which can be any one having a finite endpoint or belonging to one of the three maximum domains of attraction. We show that Value-at-Risk under extreme-value copulas is asymptotically subadditive for marginal risks with finite mean, but asymptotically superadditive for risks with infinite mean. Similar results will be discussed under the framework of Archimedean copulas in which the underlying variables need not be identically distributed.

    26 August 2020 4pm (GMT+1, London)
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    Alfred Chong (University of Illinois, USA)
    Runhuan Feng (University of Illinois, USA)
    Linfeng Zhang (University of Illinois, USA)
    Pandemic risk management: resources contingency planning and allocation
    Abstract (click to expand)

    Repeated history of pandemics such as SARS, H1N1, Ebola, Zika and COVID-19 have shown that pandemic risk is inevitable. Contingency planning is a necessary tool in the fight against pandemics. The extraordinary shortage of medical supplies in many parts of the world during the COVID-19 pandemic is attributable to the lack of coordinated efforts to build stockpiles and deploy existing resources rapidly to locations of greatest need. A combined strategy of contingency planning and resources allocation is a critical component of risk management for all organizations in the modern society. Today's technology allows us to use epidemiological models to predict the spread of infectious diseases in the similar way that meteorological models are used to forecast weather. Taking advantage of predictive models, we can project the dynamics of demand and supply for medical resources at different phases of a pandemic. Such predictions provide quantitative bases for decision makers of healthcare system to understand the potential imbalance of supply and demand, and to address disparities of access to critical medical supply across different subsidiaries and in the course of the pandemic. This talk extends the concepts of reserving and capital management in the classic insurance literature and aims to provide a quantitative framework for quantifying and assessing pandemic risk, and developing optimal strategies for resources stockpiling, emergency acquisition, and spatio-temporal resource allocations.

    Slides
    09 September 2020 1pm (GMT+1, London)
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    Ronald Richman (QED Actuaries & Consultants, South Africa) Time-Series Forecasting of Mortality Rates using Deep Learning
    Abstract (click to expand)

    In this talk, we survey recent attempts to forecast mortality rates using deep neural networks and contrast several successful approaches. Building on these, we show how time series of mortality rates can be processed using neural networks that are specialized to deal with sequential data, such as recurrent and convolutional networks. We propose a relatively simple convolutional network model for forecasting mortality rates that can be interpreted as a generalization of the Lee–Carter model, allowing for its components to be evaluated in familiar terms. This model produces highly accurate forecasts on the Human Mortality Database, and, without further modification, generalizes well to the United States Mortality Database.

    Slides
    23 September 2020 1pm (GMT+1, London)
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    Han Li (Macquarie University, Australia) Joint Extremes in Temperature and Mortality: Bivariate POT Approach
    Abstract (click to expand)

    This paper contributes to insurance risk management by modeling extreme climate risk and extreme mortality risk in an integrated manner via extreme value theory (EVT). We conduct an empirical study using monthly temperature and death data in the U.S., and find that the joint extremes in cold weather and old-age death counts exhibit the strongest level of dependence. Based on the estimated bivariate generalized Pareto distribution, we quantify the extremal dependence between death counts and temperature indexes. Methodologically, we employ the cutting edge multivariate peaks over threshold (POT) approach, which is readily applicable to a wide range of topics in extreme risk management.

    Slides
    07 October 2020 4pm (GMT+1, London)
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    Melina Mailhot (Concordia University, Canada)
    Fr??d??ric Godin (Concordia University, Canada)
    A mixed bond and equity fund model for the valuation of segregated fund policies
    Abstract (click to expand)

    Segregated fund and variable annuity policies are typically issued on mutual funds invested in both fixed income and equity asset classes. However, due to the lack of specialized models to represent the dynamics of fixed income fund returns, the literature has primarily focused on studying long-term investment guarantees on single-asset equity funds. This article develops a mixed bond and equity fund model in which the fund return is linked to movements of the yield curve. Theoretical motivation for our proposed specification is provided through an analogy with a portfolio of rolling horizon bonds. Moreover, basis risk between the portfolio return and its risk drivers is naturally incorporated into our framework. Numerical results show that the fit of our model to segregated fund data is adequate. Finally, the valuation of segregated fund policies is illustrated and it is found that the interest rate environment can have a substantial impact on guarantee costs.
    This is joint work with: Maciej Augustyniak, Emmanuel Hamel

    21 October 2020 9am (GMT+1, London)
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    Hazel Bateman (University of New South Wales, Australia) Learning to value annuities: the role of information and engagement
    Abstract (click to expand)

    Using an online experimental survey we investigate how the willingness to pay for lifetime annuities is influenced by perceptions, information framing and real world institutional settings. We find that for those participants who are engaged with the experimental retirement benefit decisions, information provision can substantially reduce or eliminate behavioural drivers of the complex task of valuation of annuities. Providing balanced information and multiple opportunities to learn about the key features of the products, including the impact of potential outcomes, narrows the gap between the willingness to pay and willingness to accept, and offsets the effects information framing, real world institutional settings and low financial capability.

    Slides
    04 November 2020 9am (UTC, London)
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    Bent Nielsen (Oxford University, UK) Generalized Log-Normal Chain-Ladder
    Abstract (click to expand)

    We propose an asymptotic theory for distribution forecasting from the log-normal chain-ladder model. The theory overcomes the difficulty of convoluting log-normal variables and takes estimation error into account. The results differ from that of the over-dispersed Poisson model and from the chain-ladder-based bootstrap. We embed the log-normal chain-ladder model in a class of infinitely divisible distributions called the generalized log-normal chain-ladder model. The asymptotic theory uses small σ asymptotics where the dimension of the reserving triangle is kept fixed while the standard deviation is assumed to decrease. The resulting asymptotic forecast distributions follow t distributions. The theory is supported by simulations and an empirical application. I will also present an application of the chain-ladder to now-casting covid deaths in the English hospitals.

    18 November 2020 3pm (UTC, London)
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    Julia Eisenberg (Vienna University of Technology, Austria) Reform proposals for occupational plans and state pension schemes.
    Abstract (click to expand)

    The increase in longevity, the ultra-low interest rates and the guarantees associated to pension benefits have put significant strain on the pension industry. Consequently, insurers need to be in a financially sound position while offering satisfactory benefits to participants. First, we discuss a pension design (for occupational and private pension plans) where the traditional guarantees are replaced by low volatility, mainly achieved by collective smoothing algorithms and an adequate asset management. Applying some optimisation techniques on the key variables of the proposed pension product, we try to achieve both a satisfactory level of the initial pension and stable pension payments over time. In the second part, we consider a reform idea for state pension schemes. The decreasing birth rates and increasing longevity threaten the sustainability of the public pension systems usually financed on a pay-as-you-go (PAYG) basis, where current contributions cover current pension expenditure. We investigate a scheme where the deficit of the PAYG system is immediately covered by the state. However, in return the individuals need to invest an amount of money into a fund. This investment is designed so that the individuals can repay "their debt" to the state at a particular level of probability and at the same time expect a positive gain. Two different strategies of debt repayment depending on the amount invested and the timing of the repayment to the state are analysed and compared to the classical PAYG scheme.

    Slides
    02 December 2020 8am (UTC, London)
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    Christian Y. Robert (ENSAE Paris Tech, CREST, France) Actuarial modeling for P2P insurance
    Abstract (click to expand)

    In this talk, an actuarial modeling based on conditional mean risk sharing is proposed to support the development of new P2P insurance offer under different business models. I will present theoretical results based on several papers written with Michel Denuit.

    Slides
    16 December 2020 3pm (UTC, London)
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    Michalis Anthropelos (University of Piraeus, Greece) On Risk-Sharing Games: Strategies, Gains and Winners
    Abstract (click to expand)

    The large majority of risk-sharing transactions involve only few counterparties. This implies that each of them could influence not only the design of the risk-sharing contracts, but also their prices. In other words, in these transactions, agents possess the market power to impact both sharing and pricing. Depending on the nature of the risk-sharing, an agent’s strategic set of choices could be associated to questions like: How much risk should I share? How much risk averse should I appear? Which subjective beliefs should I reveal in the transaction? Under oligopolistic risk-sharing settings, we establish some novel agents’ strategies based on the above questions that lead to different games among the risk-sharers. We then develop theoretical results on the induced Nash equilibria and compare them to the Pareto optimal ones. This comparison appears to have some common insightful features for all games. For example, Nash risk-sharing is different than the Pareto optimal one for any non-trivial situation and most importantly agents with relatively low risk aversion get higher gains in Nash than in Pareto equilibrium. The talk aims to present the highlights of a related series of papers and state and discuss some open research problems.

    30 December 2020 Winter Break


    Organizers

  • Jennifer Alonso García (Department of Mathematics, Université Libre de Bruxelles)
  • Munir Hiabu (Department of Mathematical Sciences, University of Copenhagen)
  • Pietro Millossovich (Cass Business School, City, University of London; DEAMS, University of Trieste)
  • Silvana Pesenti (Department of Statistical Sciences, University of Toronto)
  • Andreas Tsanakas (Cass Business School, City, University of London)
  • Andrés Villegas (School of Risk and Actuarial Studies, University of New South Wales)
  • Scientific Advisory Board

    Arnold-Gaille, Séverine (Université de Lausanne)
    Avanzi, Benjamin (University of Melbourne)
    Bauer, Daniel (University of Wisconsin Madison)
    Bergel, Agnieszka (ISEG Lisboa)
    Bernard, Carole (Grenoble Ecole of Management)
    Bignozzi, Valeria (University of Milano-Bicocca)
    Bohnert, Alexander (Technical University of Munich)
    Boonen, Tim (University of Amsterdam)
    Chen, An (Ulm University)
    Chi, Yichun (Central University of Finance and Economics)
    Constantinescu Corina (Liverpool University)
    Dhaene, Jan (KU Leuven)
    Flici, Farid (Centre for Research in Applied Economics for Development, Algeria)
    Furman, Ed (York University)
    Ghossoub, Mario (University of Waterloo)
    Guillén, Montserrat (Universidad de Barcelona)
    Hillairet, Caroline (ENSAE)
    Kaakai, Sarah (Le Mans Université)
    Khosla, Shahib (Strathmore University)
    Kleinow, Thorsten (Heriot Watt University)
    Lindholm, Mathias (Stockholm University)
    Loisel, Stéphane (ISFA, Université Lyon 1)
    Londoño, Jaime (National University of Colombia)
    Ludkovski, Mike (University of California Santa Barbara)
    MacKay, Anne (Université de Québec à Montreal)
    Richman, Ronald (QED Actuaries & Consultants)
    Shushi, Tomer (Ben-Gurion University of the Negev)
    Targino, Rodrigo S. (Getulio Vargas Foundation)
    Tzougas, George (London School of Economics)
    Vanduffel, Steven (Vrije Universiteit Brussel)
    Weke, Patrick (University of Nairobi)
    Wüthrich, Mario (ETH Zurich)

    Other Online Seminar Initiatives

  • One World Probability Seminar (One World name credit)
  • One World PDE Seminar
  • Waves in One World
  • One World Mathematical Game Theory Seminar
  • One World Seminar: Mathematical Methods for Arbitrary Data Sources
  • One World Cognitive Psychologie Seminar
  • Onew World Approximate Bayesian Computation (ABC) Seminar
  • One World IMAGing and INvErse problems (IMAGINE) Seminar
  • One World Optimization Seminar
  • One World Mathematics of INformation, Data, and Signals (MINDS) Seminar
  • One World Stochastic Numerics and Inverse Problems (SNIP) Seminar
  • Bachelier Finance Society One World Seminar
  • One World Numeration Seminar
  • One World Mathematical Physics Seminar
  • Asia-Pacific Analysis and PDE Seminar