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Stochastic differential portfolio games for an insurer in a jump-diffusion risk process

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Abstract

We discuss an optimal portfolio selection problem of an insurer who faces model uncertainty in a jump-diffusion risk model using a game theoretic approach. In particular, the optimal portfolio selection problem is formulated as a two-person, zero-sum, stochastic differential game between the insurer and the market. There are two leader-follower games embedded in the game problem: (i) The insurer is the leader of the game and aims to select an optimal portfolio strategy by maximizing the expected utility of the terminal surplus in the “worst-case” scenario; (ii) The market acts as the leader of the game and aims to choose an optimal probability scenario to minimize the maximal expected utility of the terminal surplus. Using techniques of stochastic linear-quadratic control, we obtain closed-form solutions to the game problems in both the jump-diffusion risk process and its diffusion approximation for the case of an exponential utility.

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Authors and Affiliations

  1. School of Mathematical Science and Computing Technology, Central South University, No. 22 South Shaoshan Road, Changsha, 410075, Hunan, China

    Xiang Lin & Chunhong Zhang

  2. Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW, 2109, Australia

    Tak Kuen Siu

Authors
  1. Xiang Lin
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  2. Chunhong Zhang
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  3. Tak Kuen Siu
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Corresponding author

Correspondence to Xiang Lin.

Additional information

This research was supported by the national Natural Science Foundation of China (project no. 11071258 and 90820302) and the Fundamental Research Funds for the Central Universities (project no. 2010QYZD001).

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Lin, X., Zhang, C. & Siu, T.K. Stochastic differential portfolio games for an insurer in a jump-diffusion risk process. Math Meth Oper Res 75, 83–100 (2012). https://doi.org/10.1007/s00186-011-0376-z

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  • DOI: https://doi.org/10.1007/s00186-011-0376-z

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