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An optimal reinsurance problem in the Cramér–Lundberg model

Author

Listed:
  • Arian Cani

    (Université de Lausanne)

  • Stefan Thonhauser

    (Graz University of Technology)

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.

Suggested Citation

  • Arian Cani & Stefan Thonhauser, 2017. "An optimal reinsurance problem in the Cramér–Lundberg model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(2), pages 179-205, April.
    • Handle: RePEc:spr:mathme:v:85:y:2017:i:2:d:10.1007_s00186-016-0559-8
    DOI: 10.1007/s00186-016-0559-8
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    References listed on IDEAS

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    Cited by:

    1. Preischl, M. & Thonhauser, S., 2019. "Optimal reinsurance for Gerber–Shiu functions in the Cramér–Lundberg model," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 82-91.

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