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Optimal non-proportional reinsurance control and stochastic differential games

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  • Taksar, Michael
  • Zeng, Xudong
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    Abstract

    We study stochastic differential games between two insurance companies who employ reinsurance to reduce risk exposure. We consider competition between two companies and construct a single payoff function of two companies' surplus processes. One company chooses a dynamic reinsurance strategy in order to maximize the payoff function while its opponent is simultaneously choosing a dynamic reinsurance strategy so as to minimize the same quantity. We describe the Nash equilibrium of the game and prove a verification theorem for a general payoff function. For the payoff function being the probability that the difference between two surplus reaches an upper bound before it reaches a lower bound, the game is solved explicitly.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 48 (2011)
    Issue (Month): 1 (January)
    Pages: 64-71

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    Handle: RePEc:eee:insuma:v:48:y:2011:i:1:p:64-71

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Non-proportional reinsurance HJB equation Ruin probability Stochastic control Stochastic differential game;

    References

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    1. Hipp, Christian & Taksar, Michael, 2010. "Optimal non-proportional reinsurance control," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 246-254, October.
    2. Zeng, Xudong, 2010. "Optimal reinsurance with a rescuing procedure," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 397-405, April.
    3. Michael I. Taksar, 2000. "Optimal risk and dividend distribution control models for an insurance company," Computational Statistics, Springer, Springer, vol. 51(1), pages 1-42, 02.
    4. Suijs, J.P.M. & De Waegenaere, A.M.B. & Borm, P.E.M., 1998. "Stochastic cooperative games in insurance and reinsurance," Open Access publications from Tilburg University urn:nbn:nl:ui:12-77120, Tilburg University.
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    Cited by:
    1. Jin, Zhuo & Yin, G. & Wu, Fuke, 2013. "Optimal reinsurance strategies in regime-switching jump diffusion models: Stochastic differential game formulation and numerical methods," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 733-746.
    2. Luo, Shangzhen & Taksar, Michael, 2012. "Minimal cost of a Brownian risk without ruin," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 685-693.
    3. Xiang Lin & Chunhong Zhang & Tak Siu, 2012. "Stochastic differential portfolio games for an insurer in a jump-diffusion risk process," Computational Statistics, Springer, Springer, vol. 75(1), pages 83-100, February.
    4. Christophe Dutang & Hansjoerg Albrecher & Stéphane Loisel, 2013. "Competition among non-life insurers under solvency constraints: A game-theoretic approach," Post-Print hal-00746245, HAL.

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