BEGIN:VCALENDAR
VERSION:2.0
BEGIN:VEVENT
CLASS:PUBLIC
DESCRIPTION:Speakers: Nora Muler (Universidad Torcuato Di Tella\, Argentina)\n\nTitle: Optimal dividend payment under constraints\n\nAbstract: 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.\n This is a joint work with Hansjoerg Albrecher and Pablo Azcue.\n\nFurther details: https://owars.info\n\nThe zoom link will be available 15 minutes before the seminar on the following link: https://docs.google.com/document/d/1ExsaDqghA0zJZZ-V4mBIT50W3_jmDJznfirjyz-EzC8/edit?ts=5e9f9a01\n
DTSTART:20210901T150000Z
DTEND:20210901T161000Z
LOCATION:https://docs.google.com/document/d/1ExsaDqghA0zJZZ-V4mBIT50W3_jmDJznfirjyz-EzC8/edit?ts=5e9f9a01
SUMMARY;LANGUAGE=en-us:[OWARS] Nora Muler (Universidad Torcuato Di Tella, Argentina)
END:VEVENT
END:VCALENDAR