Budget-Constrained Optimal Reinsurance Design Under Coherent Risk Measures

25 Pages Posted: 30 Nov 2017

See all articles by Ka Chun Cheung

Ka Chun Cheung

The University of Hong Kong

Wing Fung Chong

Heriot-Watt University - Department of Actuarial Mathematics and Statistics

Ambrose Lo

University of Iowa - Department of Statistics & Actuarial Science

Date Written: November 26, 2017

Abstract

Reinsurance is a versatile risk management strategy commonly employed by insurers to optimize their risk profile. In this paper, we study an optimal reinsurance design problem minimizing a general law-invariant coherent risk measure of the net risk exposure of a generic insurer, in conjunction with a general law-invariant comonotonic additive convex reinsurance premium principle and a premium budget constraint. Due to its intrinsic generality, this contract design problem encompasses a wide body of optimal reinsurance models encountered in practice. A three-step solution scheme is presented. Firstly, the objective and constraint functions are exhibited in the so-called Kusuoka's integral representations. Secondly, the mini-max theorem for infinite dimensional spaces is applied to interchange the infimum on the space of indemnities and the supremum on the space of probability measures. Thirdly, the recently developed Neyman-Pearson methodology due to Lo (2017) is adopted to solve the resulting infimum problem. Analytic and transparent expressions for the optimal reinsurance policy are provided, followed by illustrative examples.

Keywords: Budget constraint; Distortion; TVaR; Mini-max Theorem; Neyman-Pearson

JEL Classification: G22; C61

Suggested Citation

Cheung, Ka Chun and Chong, Wing Fung and Lo, Ambrose, Budget-Constrained Optimal Reinsurance Design Under Coherent Risk Measures (November 26, 2017). Available at SSRN: https://ssrn.com/abstract=3077653 or http://dx.doi.org/10.2139/ssrn.3077653

Ka Chun Cheung

The University of Hong Kong ( email )

Pokfulam Road
Hong Kong, Pokfulam HK
China

Wing Fung Chong (Contact Author)

Heriot-Watt University - Department of Actuarial Mathematics and Statistics ( email )

Edinburgh, Scotland EH14 4AS
United Kingdom

Ambrose Lo

University of Iowa - Department of Statistics & Actuarial Science ( email )

Iowa City, IA 52242-1409
United States

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