Pareto-optimal reinsurance under individual risk constraints

Mario Ghossoub, Wenjun Jiang and Jiandong Ren

Insurance: Mathematics and Economics, 2022, vol. 107, issue C, 307-325

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.

Keywords: Reinsurance; Pareto optimality; Risk constraints; Distortion risk measures; Range Value-at-Risk (search for similar items in EconPapers)
JEL-codes: C71 G22 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:107:y:2022:i:c:p:307-325

DOI: 10.1016/j.insmatheco.2022.09.003

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