Optimal Reinsurance with Expectile

Cai, J., Weng, C. (2016). Optimal reinsurance with expectile. Scandinavian Actuarial Journal 2016(7), 624-645.

27 Pages Posted: 6 Feb 2017

See all articles by Jun Cai

Jun Cai

University of Waterloo - Department of Statistics and Actuarial Science

Chengguo Weng

University of Waterloo; University of Waterloo - Department of Statistics and Actuarial Science

Date Written: 2014

Abstract

In this paper, we study optimal reinsurance treaties that minimize the liability of an insurer. The liability is defined as the actuarial reserve on an insurer's risk exposure plus the risk margin required for the risk exposure. The risk margin is determined by the risk measure of expectile. Among a general class of reinsurance premium principles, we prove that a two-layer reinsurance treaty is optimal. Furthermore, if a reinsurance premium principle in the class is translation invariant or is the expected value principle, we show that a one-layer reinsurance treaty is optimal. Moreover, we use the expected value premium principle and Wang's premium principle to demonstrate how the parameters in an optimal reinsurance treaty can be determined explicitly under a given premium principle.

Keywords: Reinsurance, Risk measure, Expectile, Coherent, Elicitable, Premium principle, Actuarial reserve, Risk margin, Liability

Suggested Citation

Cai, Jun and Weng, Chengguo, Optimal Reinsurance with Expectile (2014). Cai, J., Weng, C. (2016). Optimal reinsurance with expectile. Scandinavian Actuarial Journal 2016(7), 624-645., Available at SSRN: https://ssrn.com/abstract=2912030

Jun Cai

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Chengguo Weng (Contact Author)

University of Waterloo ( email )

M3-200 Univ Ave W
Waterloo, Ontario N2L3G1
Canada
(1)888-4567 ext.31132 (Phone)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Croatia

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