On Pareto-Optimal Reinsurance with Constraints Under Distortion Risk Measures

27 Pages Posted: 20 Apr 2017

See all articles by Wenjun Jiang

Wenjun Jiang

University of Calgary

Hanping Hong

University of Western Ontario

Jiandong Ren

University of Western Ontario

Date Written: March 28, 2017

Abstract

This paper studies the Pareto-optimal reinsurance policies, where both the insurer's and the reinsurer's risks and returns are considered. We assume that the risks of the insurer and the reinsurer, as well as the reinsurance premium, are determined by some distortion risk measures with different distortion operators. Under the constraint that a reinsurance policy is feasible only if the resulting risk of each party is below some pre-determined values, we derive explicit expressions for the optimal reinsurance polices. Methodologically, we show that the generalized Neyman-Pearson method, the Lagrange multiplier method, and the dynamic control methods can be utilized to solve the optimization problem with constraints. Special cases when both parties' risks are measured by Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) are studied in great details. Numerical examples are provided to illustrate practical implications of the results.

Keywords: Pareto-optimal reinsurance, distortion risk measure, constraints, Value-at-Risk, Tail Value-at-Risk

Suggested Citation

Jiang, Wenjun and Hong, Hanping and Ren, Jiandong, On Pareto-Optimal Reinsurance with Constraints Under Distortion Risk Measures (March 28, 2017). Available at SSRN: https://ssrn.com/abstract=2955764 or http://dx.doi.org/10.2139/ssrn.2955764

Wenjun Jiang (Contact Author)

University of Calgary ( email )

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

Hanping Hong

University of Western Ontario

1151 Richmond Street
Suite 2
London, Ontario N6A 5B8
Canada

Jiandong Ren

University of Western Ontario ( email )

1151 Richmond Street
Suite 2
London, Ontario N6A 5B8
Canada

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