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

Michael Julius Preischl, Stefan Thonhauser

Research output: Contribution to journalArticlepeer-review


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.

Translated title of the contributionOptimale Rückversicherung für Gerber Shiu Funktionen im Cramér-Lundberg Model
Original languageEnglish
Pages (from-to)82-91
Number of pages10
JournalInsurance / Mathematics & economics
Issue number87
Early online dateApr 2019
Publication statusPublished - 2019


  • Cramér-Lundberg model
  • Dynamic reinsurance
  • Gerber–Shiu functions
  • Optimal stochastic control
  • Policy iteration

ASJC Scopus subject areas

  • Economics and Econometrics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fields of Expertise

  • Information, Communication & Computing


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