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Optimal reinsurance for Gerber-Shiu functions in the Cramér-Lundberg model. (English) Zbl 1410.91282

Summary: 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.

MSC:

91B30 Risk theory, insurance (MSC2010)
93E20 Optimal stochastic control
60K10 Applications of renewal theory (reliability, demand theory, etc.)
60J75 Jump processes (MSC2010)
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References:

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