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

Michael Preischl and Stefan Thonhauser

Papers from arXiv.org

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.

Date: 2018-09
New Economics Papers: this item is included in nep-dge and nep-rmg
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