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Optimal reinsurance with multiple tranches

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  • Malamud, Semyon
  • Rui, Huaxia
  • Whinston, Andrew

Abstract

Motivated by common practices in the reinsurance industry and in insurance markets such as Lloyd’s, we study the general problem of optimal insurance contracts design in the presence of multiple insurance providers. We show that the optimal risk allocation rule is characterized by a hierarchical structure of risk sharing where all agents take on risks only above the endogenously determined thresholds, or agent-specific deductibles. Linear risk sharing between two adjacent thresholds is shown to be optimal when all agents have CARA utilities. Furthermore, we show that the optimal thresholds can be efficiently calculated through the fixed point of a contraction mapping.

Suggested Citation

  • Malamud, Semyon & Rui, Huaxia & Whinston, Andrew, 2016. "Optimal reinsurance with multiple tranches," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 71-82.
    • Handle: RePEc:eee:mateco:v:65:y:2016:i:c:p:71-82
    DOI: 10.1016/j.jmateco.2016.05.006
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    References listed on IDEAS

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    Cited by:

    1. Reichel, Lukas & Schmeiser, Hato & Schreiber, Florian, 2022. "On the optimal management of counterparty risk in reinsurance contracts," Journal of Economic Behavior & Organization, Elsevier, vol. 201(C), pages 374-394.
    2. Albrecher, Hansjörg & Cani, Arian, 2019. "On randomized reinsurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 67-78.
    3. Susan F. Lu & Huaxia Rui & Abraham Seidmann, 2018. "Does Technology Substitute for Nurses? Staffing Decisions in Nursing Homes," Management Science, INFORMS, vol. 64(4), pages 1842-1859, April.
    4. Reichel, Lukas & Schmeiser, Hato & Schreiber, Florian, 2021. "Sometimes more, sometimes less: Prudence and the diversification of risky insurance coverage," European Journal of Operational Research, Elsevier, vol. 292(2), pages 770-783.

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