Optimal Reinsurance in a Market of Multiple Reinsurers Under Law-Invariant Convex Risk Measures

23 Pages Posted: 2 Nov 2017

See all articles by Jun Cai

Jun Cai

University of Waterloo - Department of Statistics and Actuarial Science

Christiane Lemieux

University of Waterloo - Department of Statistics and Actuarial Science

Fangda Liu

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

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: October 31, 2017

Abstract

It is natural to connect reinsurance problems with risk measures since a reinsurance contract is an efficient risk management tool for an insurer and the reinsurance premium can also be viewed as a measure of a reinsurer's risk. In this paper, we assume that the insurer uses a law-invariant convex risk measure, while reinsurers use a Wang's premium principle to determine their premiums. We study an optimal reinsurance policy design from an insurer's perspective in a market of multiple reinsurers. Both the insurer's risk measure and the reinsurer's premium principle represent broad families of risk measures with considerable generality. We provide a general formula for the optimal solution which recovers existing results if particular law-invariant convex measures, such as the AVaR, and particular premium principles are assigned.

Keywords: Optimal reinsurance design, convex risk measure, Wang's premium principle

Suggested Citation

Cai, Jun and Lemieux, Christiane and Liu, Fangda and Liu, Fangda and Wang, Ruodu, Optimal Reinsurance in a Market of Multiple Reinsurers Under Law-Invariant Convex Risk Measures (October 31, 2017). Available at SSRN: https://ssrn.com/abstract=3062767 or http://dx.doi.org/10.2139/ssrn.3062767

Jun Cai

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

Waterloo, Ontario N2L 3G1
Canada

Christiane Lemieux

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

Waterloo, Ontario N2L 3G1
Canada

Fangda Liu (Contact Author)

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

Waterloo, Ontario N2L 3G1
Canada

Georgia State University ( email )

35 Broad St NW
Apt 1110
Atlanta, GA 30303
United States
4703789998 (Phone)

Ruodu Wang

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

Waterloo, Ontario N2L 3G1
Canada

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