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Stackelberg differential game for insurance under model ambiguity

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  • Cao, Jingyi
  • Li, Dongchen
  • Young, Virginia R.
  • Zou, Bin

Abstract

We study a dynamic Stackelberg differential game between a buyer and a seller of insurance policies in a spectrally negative Lévy framework, in which both parties are ambiguous about the intensity and severity of insurable losses. Both the buyer and seller aim to maximize their expected wealth, plus a penalty term that reflects ambiguity, over an exogenous random horizon. Under a mean-variance premium principle and a quadratic penalty for ambiguity, we obtain the equilibrium in closed form. Our main results show that the buyer's robust optimal indemnity is a coinsurance with proportion less than one-half, which increases (resp. decreases) as the buyer (resp. seller) becomes more ambiguity averse. Also we show that the seller's robust optimal premium rule equals the net premium under the buyer's optimally distorted probability, which is the buyer's “best hope,” and it exceeds the actuarially fair premium under the seller's optimally distorted probability measure so is, thereby, acceptable to the seller.

Suggested Citation

  • Cao, Jingyi & Li, Dongchen & Young, Virginia R. & Zou, Bin, 2022. "Stackelberg differential game for insurance under model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 128-145.
    • Handle: RePEc:eee:insuma:v:106:y:2022:i:c:p:128-145
    DOI: 10.1016/j.insmatheco.2022.06.003
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    References listed on IDEAS

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    Cited by:

    1. Zhu, Michael B. & Ghossoub, Mario & Boonen, Tim J., 2023. "Equilibria and efficiency in a reinsurance market," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 24-49.
    2. David Landriault & Bin Li & Hong Li & Yuanyuan Zhang, 2024. "Contract Structure and Risk Aversion in Longevity Risk Transfers," Papers 2409.08914, arXiv.org.
    3. Guillermo Alvarez & Ibrahim Ekren & Anastasis Kratsios & Xuwei Yang, 2024. "Neural Operators Can Play Dynamic Stackelberg Games," Papers 2411.09644, arXiv.org.
    4. Ghossoub, Mario & Zhu, Michael B., 2024. "Stackelberg equilibria with multiple policyholders," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 189-201.
    5. Cao, Jingyi & Li, Dongchen & Young, Virginia R. & Zou, Bin, 2023. "Reinsurance games with two reinsurers: Tree versus chain," European Journal of Operational Research, Elsevier, vol. 310(2), pages 928-941.

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    More about this item

    Keywords

    Stackelberg differential game; Insurance; Ambiguity; Mean-variance premium principle; Random time horizon;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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