Optimale Rückversicherung für Gerber Shiu Funktionen im Cramér-Lundberg Model

Michael Julius Preischl, Stefan Thonhauser

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

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.

Titel in ÜbersetzungOptimale Rückversicherung für Gerber Shiu Funktionen im Cramér-Lundberg Model
Originalspracheenglisch
Seiten (von - bis)82-91
Seitenumfang10
FachzeitschriftInsurance / Mathematics & economics
Jahrgang87
Ausgabenummer87
Frühes Online-DatumApr 2019
DOIs
PublikationsstatusVeröffentlicht - 2019

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Gerber-Shiu Function
Reinsurance
Optimal Stochastic Control
Ruin Probability
Control Function
Penalty Function
Existence and Uniqueness
Minimise
Numerical Examples
Model
Ruin probability
Expected discounted penalty function
Optimal reinsurance
Stochastic optimal control
Control function
Uniqueness
Gerber-Shiu function
Strategy

Schlagwörter

    ASJC Scopus subject areas

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

    Fields of Expertise

    • Information, Communication & Computing

    Dies zitieren

    Optimal reinsurance for Gerber–Shiu functions in the Cramér–Lundberg model. / Preischl, Michael Julius; Thonhauser, Stefan.

    in: Insurance / Mathematics & economics, Jahrgang 87, Nr. 87, 2019, S. 82-91.

    Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

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