Pareto-optimal Reinsurance Under Individual Risk Constraints

27 Pages Posted: 30 Dec 2021

See all articles by Mario Ghossoub

Mario Ghossoub

University of Waterloo

Wenjun Jiang

University of Calgary

Jiandong Ren

University of Western Ontario

Date Written: December 28, 2021


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. We 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

JEL Classification: C71, G22

Suggested Citation

Ghossoub, Mario and Jiang, Wenjun and Ren, Jiandong, Pareto-optimal Reinsurance Under Individual Risk Constraints (December 28, 2021). Available at SSRN: or

Mario Ghossoub (Contact Author)

University of Waterloo ( email )

Dept. of Statistics & Actuarial Science
200 University Ave. W.
Waterloo, Ontario N2L 3G1


Wenjun Jiang

University of Calgary ( email )

612 Campus Place N.W.
University of Calgary
Calgary, Alberta T2N 1N4

Jiandong Ren

University of Western Ontario ( email )

1151 Richmond Street
Suite 2
London, Ontario N6A 5B8

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