An optimal reinsurance problem in the Cramér–Lundberg model

Arian Cani () and Stefan Thonhauser ()
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Arian Cani: Université de Lausanne
Stefan Thonhauser: Graz University of Technology

Mathematical Methods of Operations Research, 2017, vol. 85, issue 2, No 2, 179-205

Abstract: Abstract In this article we consider the surplus process of an insurance company within the Cramér–Lundberg framework with the intention of controlling its performance by means of dynamic reinsurance. Our aim is to find a general dynamic reinsurance strategy that maximizes the expected discounted surplus level integrated over time. Using analytical methods we identify the value function as a particular solution to the associated Hamilton–Jacobi–Bellman equation. This approach leads to an implementable numerical method for approximating the value function and optimal reinsurance strategy. Furthermore we give some examples illustrating the applicability of this method for proportional and XL-reinsurance treaties.

Keywords: Cramér–Lundberg model; Reinsurance; Stochastic control (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00186-016-0559-8

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