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Optimal dynamic reinsurance policies for large insurance portfolios

Author

Listed:
  • Charlotte Markussen

    (Laboratory of Actuarial Mathematics, Copenhagen University, Universitetsparken 5, 2100 Copenhagen, Denmark Manuscript)

  • Michael I. Taksar

    (Department of Applied Mathematics, State University of New York at Stony Brook, Stony Brook, NY 11794-3600, USA)

Abstract

We consider a large insurance company whose surplus (reserve) is modeled by a Brownian motion. The company invests its surplus in stock market assets which may or may not contain an element of risk. To minimize the insurance risk there is a possibility to reinsure a part or the whole insurance portfolio. We consider the case of proportional reinsurance. There is a transaction cost, which manifests itself in the fact that the safety loading of the reinsurer is larger than that of the cedent. Stochastic optimal control theory is used to determine the optimal reinsurance policy which minimizes the ruin probability of the cedent.

Suggested Citation

  • Charlotte Markussen & Michael I. Taksar, 2003. "Optimal dynamic reinsurance policies for large insurance portfolios," Finance and Stochastics, Springer, vol. 7(1), pages 97-121.
    • Handle: RePEc:spr:finsto:v:7:y:2003:i:1:p:97-121
    Note: received: February 2001; final version received: February 2002
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    More about this item

    Keywords

    Stochastic control; stochastic differential equations; Black-Scholes model; controlled stochastic processes. proportional reinsurance; investments; ruin probabilities;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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