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Pareto-optimal reinsurance under individual risk constraints

Author

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  • Ghossoub, Mario
  • Jiang, Wenjun
  • Ren, Jiandong

Abstract

This paper studies the design of Pareto-optimal reinsurance contracts in a market where the insurer and reinsurer maximize their expected utilities of end-of-period wealth. In addition, we assume that the insurer and reinsurer wish to control their solvency risks, which are defined through distortion risk measures of their end-of-period risk exposures. To prevent ex post moral hazard, the no-sabotage condition is exogenously imposed on the set of ex ante admissible indemnity functions. By adopting piece-wise linear distortion functions for the risk measures, we partition the domain of the loss into disjoint pieces as per the features of distortion functions and then derive the parametric form of the optimal indemnity function over each piece, where the parameters are left for numerical optimizations. A concrete example where both the insurer and reinsurer apply Range Value-at-Risk is studied in detail.

Suggested Citation

  • Ghossoub, Mario & Jiang, Wenjun & Ren, Jiandong, 2022. "Pareto-optimal reinsurance under individual risk constraints," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 307-325.
    • Handle: RePEc:eee:insuma:v:107:y:2022:i:c:p:307-325
    DOI: 10.1016/j.insmatheco.2022.09.003
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Reinsurance; Pareto optimality; Risk constraints; Distortion risk measures; Range Value-at-Risk;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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