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Optimal Reinsurance for Gerber-Shiu Functions in the Cramer-Lundberg Model (1809.00990v1)
Published 4 Sep 2018 in math.OC and q-fin.PM
Abstract: Complementing existing results on minimal ruin probabilities, we minimize expected discounted penalty functions (or Gerber-Shiu functions) in a Cramer-Lundberg model by choosing optimal reinsurance. Reinsurance strategies are modelled as time dependant control functions, which leads to a setting from the theory of optimal stochastic control and ultimately to the problem's Hamilton-Jacobi-BeLLMan equation. We show existence and uniqueness of the solution found by this method and provide numerical examples involving light and heavy tailed claims and also give a remark on the asymptotics.