Optimal reinsurance for Gerber–Shiu functions in the Cramér–Lundberg model

M. Preischl and S. Thonhauser

Insurance: Mathematics and Economics, 2019, vol. 87, issue C, 82-91

Abstract: Complementing existing results on minimal ruin probabilities, we minimize expected discounted penalty functions (or Gerber–Shiu functions) in a Cramér–Lundberg model by choosing optimal reinsurance. Reinsurance strategies are modeled as time dependent control functions, which lead 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.

Keywords: Dynamic reinsurance; Optimal stochastic control; Gerber–Shiu functions; Policy iteration; Cramér-Lundberg model (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:87:y:2019:i:c:p:82-91

DOI: 10.1016/j.insmatheco.2019.04.002

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