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Necessary and Sufficient Optimality Conditions for Regular–Singular Stochastic Differential Games with Asymmetric Information

Author

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  • Yan Wang

    (Dalian Jiaotong University)

  • Lei Wang

    (Dalian University of Technology)

  • Kok Lay Teo

    (Curtin University)

Abstract

We consider a class of regular–singular stochastic differential games arising in the optimal investment and dividend problem of an insurer under model uncertainty. The information available to the two players is asymmetric partial information and the control variable of each player consists of two components: regular control and singular control. We establish the necessary and sufficient optimality conditions for the saddle point of the zero-sum game. Then, as an application, these conditions are applied to an optimal investment and dividend problem of an insurer under model uncertainty. Furthermore, we generalize our results to the nonzero-sum regular–singular game with asymmetric information, and then the Nash equilibrium point is characterized.

Suggested Citation

  • Yan Wang & Lei Wang & Kok Lay Teo, 2018. "Necessary and Sufficient Optimality Conditions for Regular–Singular Stochastic Differential Games with Asymmetric Information," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 501-532, November.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:2:d:10.1007_s10957-018-1251-3
    DOI: 10.1007/s10957-018-1251-3
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    References listed on IDEAS

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    Cited by:

    1. Dianetti, Jodi & Ferrari, Giorgio, 2019. "Nonzero-Sum Submodular Monotone-Follower Games. Existence and Approximation of Nash Equilibria," Center for Mathematical Economics Working Papers 605, Center for Mathematical Economics, Bielefeld University.
    2. Puru Gupta & Saul D. Jacka, 2023. "Portfolio Choice In Dynamic Thin Markets: Merton Meets Cournot," Papers 2309.16047, arXiv.org.
    3. Dianetti, Jodi, 2023. "Linear-Quadratic-Singular Stochastic Differential Games and Applications," Center for Mathematical Economics Working Papers 678, Center for Mathematical Economics, Bielefeld University.

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