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A mean field game approach to optimal investment and risk control for competitive insurers

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  • Bo, Lijun
  • Wang, Shihua
  • Zhou, Chao

Abstract

We consider an insurance market consisting of multiple competitive insurers with a mean field interaction via their terminal wealth under the exponential utility with relative performance. It is assumed that each insurer regulates her risk by controlling the number of policies. We respectively establish the constant Nash equilibrium (independent of time) on the investment and risk control strategy for the finite n-insurer game and the constant mean field equilibrium for the corresponding mean field game (MFG) problem (when the number of insurers tends to infinity). Furthermore, we examine the convergence relationship between the constant Nash equilibrium of finite n-insurer game and the mean field equilibrium of the corresponding MFG problem. Our numerical analysis reveals that, for a highly competitive insurance market consisting of many insurers, every insurer will invest more in risky assets and increase the total number of outstanding liabilities to maximize her exponential utility with relative performance.

Suggested Citation

  • Bo, Lijun & Wang, Shihua & Zhou, Chao, 2024. "A mean field game approach to optimal investment and risk control for competitive insurers," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 202-217.
    • Handle: RePEc:eee:insuma:v:116:y:2024:i:c:p:202-217
    DOI: 10.1016/j.insmatheco.2024.03.002
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    References listed on IDEAS

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    More about this item

    Keywords

    Competitive insurers; Investment and risk control; Mean field interaction; Nash equilibrium; Mean field game;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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