One World Actuarial Research Seminar

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.

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.

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.

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).

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.

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.

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

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.

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.

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.

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.

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

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.

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.

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.

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.

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.