Optimal Reinsurance for Gerber-Shiu Functions in the Cramer-Lundberg\n Model

2018/09/04 by Michael Preischl, Preischl, Michael, Stefan Thonhauser +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #60J75 #93E20 #FOS: Economics and business #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1809.00990

openalex publication_date 2018/09/04 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28

Abstract

Complementing existing results on minimal ruin probabilities, we minimize\nexpected discounted penalty functions (or Gerber-Shiu functions) in a\nCramer-Lundberg model by choosing optimal reinsurance. Reinsurance strategies\nare modelled as time dependant control functions, which leads to a setting from\nthe theory of optimal stochastic control and ultimately to the problem's\nHamilton-Jacobi-Bellman equation. We show existence and uniqueness of the\nsolution found by this method and provide numerical examples involving light\nand heavy tailed claims and also give a remark on the asymptotics.\n

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