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Reinsurance games with two reinsurers: Tree versus chain

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

Abstract

This paper studies reinsurance contracting and competition in a continuous-time model with ambiguity. The market consists of one insurer and two reinsurers, who apply a generalized expected-value premium principle and a generalized variance premium principle to price reinsurance contracts, respectively. The reinsurance contracting problems between the insurer and reinsurers are resolved by Stackelberg differential games, and the reinsurance competition between two reinsurers is settled by a non-cooperative Nash game. We obtain the closed-form equilibrium strategies for all three players under both a tree structure and a chain structure. A detailed comparison study reveals that the tree structure is preferred to the chain structure from a social planner’s perspective, and the tree structure is generally preferred from the insurer’s perspective.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:310:y:2023:i:2:p:928-941
    DOI: 10.1016/j.ejor.2023.04.005
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    2. Zongxia Liang & Yi Xia & Bin Zou, 2024. "A Two-layer Stochastic Game Approach to Reinsurance Contracting and Competition," Papers 2405.06235, arXiv.org, revised Sep 2024.
    3. Yoshioka, Hidekazu & Yoshioka, Yumi, 2024. "Assessing fluctuations of long-memory environmental variables based on the robustified dynamic Orlicz risk," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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    More about this item

    Keywords

    Game theory; Stackelberg differential game; Non-cooperative Nash game; Optimal reinsurance; Ambiguity;
    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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