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Optimal reinsurance with multiple reinsurers: Competitive pricing and coalition stability

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  • Boonen, Tim J.
  • Tan, Ken Seng
  • Zhuang, Sheng Chao

Abstract

This paper studies economic pricing of reinsurance contracts via competition of an insurer with multiple reinsurers. All firms are assumed to be endowed with distortion risk measures or expected exponential utilities. Reinsurance contracts are required to be Pareto optimal, individually rational, and satisfy a competition constraint that we call coalition stability. As shown in the literature, it holds that Pareto optimality is equivalent to a structure on the indemnities. This paper characterizes the corresponding premiums by a competition argument. The competition among reinsurers imposes constraints on the premiums that the reinsurers are able to charge and this may lead to a strictly positive profit for the insurer. When the firms use distortion risk measures, this constraint yields stability for subcoalitions, which is a condition akin to the core in cooperative game theory. The premiums and the profit of the insurer are derived in closed-form. This paper illustrates this premium function with the Mean Conditional Value-at-Risk and the GlueVaR. If the firms use expected exponential utilities, the premium is represented by an exponential premium.

Suggested Citation

  • Boonen, Tim J. & Tan, Ken Seng & Zhuang, Sheng Chao, 2021. "Optimal reinsurance with multiple reinsurers: Competitive pricing and coalition stability," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 302-319.
    • Handle: RePEc:eee:insuma:v:101:y:2021:i:pb:p:302-319
    DOI: 10.1016/j.insmatheco.2021.08.005
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    References listed on IDEAS

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    Cited by:

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    3. Meng, Hui & Wei, Li & Zhou, Ming, 2023. "Multiple per-claim reinsurance based on maximizing the Lundberg exponent," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 33-47.

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    More about this item

    Keywords

    Reinsurance; Multiple reinsurers; Competition; Premiums; Mean Conditional Value-at-Risk; GlueVaR;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition

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