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Optimal non-proportional reinsurance control and stochastic differential games

Author

Listed:
  • Taksar, Michael
  • Zeng, Xudong

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.

Suggested Citation

  • Taksar, Michael & Zeng, Xudong, 2011. "Optimal non-proportional reinsurance control and stochastic differential games," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 64-71, January.
  • Handle: RePEc:eee:insuma:v:48:y:2011:i:1:p:64-71
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    References listed on IDEAS

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    1. Suijs, J.P.M. & De Waegenaere, A.M.B. & Borm, P.E.M., 1996. "Stochastic Cooperative Games in Insurance and Reinsurance," Discussion Paper 1996-53, Tilburg University, Center for Economic Research.
    2. Suijs, Jeroen & De Waegenaere, Anja & Borm, Peter, 1998. "Stochastic cooperative games in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 209-228, July.
    3. repec:spr:compst:v:51:y:2000:i:1:p:1-42 is not listed on IDEAS
    4. Zeng, Xudong, 2010. "Optimal reinsurance with a rescuing procedure," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 397-405, April.
    5. Hipp, Christian & Taksar, Michael, 2010. "Optimal non-proportional reinsurance control," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 246-254, October.
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    Citations

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    Cited by:

    1. repec:spr:compst:v:75:y:2012:i:1:p:83-100 is not listed on IDEAS
    2. 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.
    3. repec:eee:insuma:v:75:y:2017:i:c:p:58-70 is not listed on IDEAS
    4. Xiang Lin & Chunhong Zhang & Tak Siu, 2012. "Stochastic differential portfolio games for an insurer in a jump-diffusion risk process," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(1), pages 83-100, February.
    5. Luo, Shangzhen & Taksar, Michael, 2012. "Minimal cost of a Brownian risk without ruin," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 685-693.
    6. repec:mje:mjejnl:v:12:y:2016:i:3:p:87-100 is not listed on IDEAS
    7. repec:eee:ejores:v:264:y:2018:i:3:p:1144-1158 is not listed on IDEAS
    8. Meng, Hui & Li, Shuanming & Jin, Zhuo, 2015. "A reinsurance game between two insurance companies with nonlinear risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 91-97.
    9. Dutang, Christophe & Albrecher, Hansjoerg & Loisel, Stéphane, 2013. "Competition among non-life insurers under solvency constraints: A game-theoretic approach," European Journal of Operational Research, Elsevier, vol. 231(3), pages 702-711.

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