Risk Measures Induced by Efficient Insurance Contracts

26 Pages Posted: 6 Oct 2021 Last revised: 10 Jan 2022

See all articles by Qiuqi Wang

Qiuqi Wang

University of Waterloo - Department of Statistics and Actuarial Science

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Ricardas Zitikis

Western University

Date Written: September 1, 2021

Abstract

The Expected Shortfall (ES) is one of the most important regulatory risk measures in finance, insurance, and statistics, which has recently been characterized via sets of axioms from perspectives of portfolio risk management and statistics. Meanwhile, there is large literature on insurance design with ES as an objective or a constraint. A visible gap is to justify the special role of ES in insurance and actuarial science. To fill this gap, we study the characterization of risk measures induced by efficient insurance contracts, i.e., those that are Pareto optimal for the insured and the insurer. One of our major results is that we characterize a mixture of the mean and ES as the risk measure of the insured and the insurer, when contracts with deductibles are efficient. Characterization results of other risk measures, including the mean and distortion risk measures, are also presented by linking them to different sets of contracts.

Keywords: Optimal insurance, Expected Shortfall, Pareto optimality, deductible, concentration

JEL Classification: C02,C5,C6,C7,D8,G2

Suggested Citation

Wang, Qiuqi and Wang, Ruodu and Zitikis, Ricardas, Risk Measures Induced by Efficient Insurance Contracts (September 1, 2021). Insurance: Mathematics and Economics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3915592 or http://dx.doi.org/10.2139/ssrn.3915592

Qiuqi Wang (Contact Author)

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

Waterloo, Ontario N2L 3G1
Canada

Ruodu Wang

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

Waterloo, Ontario N2L 3G1
Canada

Ricardas Zitikis

Western University ( email )

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

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