Mean-Variance Insurance Design with Counterparty Risk and Incentive Compatibility

ASTIN Bulletin, 2022

24 Pages Posted: 28 Jul 2021 Last revised: 6 Feb 2024

See all articles by Tim J. Boonen

Tim J. Boonen

University of Hong Kong

Wenjun Jiang

University of Calgary

Date Written: February 3, 2022

Abstract

This paper studies the optimal insurance design from the perspective of an insured when there is possibility for the insurer to default on its promised indemnity. Default of the insurer leads to limited liability, and the promised indemnity is only partially recovered in case of a default. To alleviate the potential ex post moral hazard, an incentive compatibility condition is added to restrict the permissible indemnity function. Under the actuarial premium principle and mean-variance preferences of the insured, we derive the explicit structure of the optimal indemnity function through the marginal indemnity function formulation of the problem. It is shown that the optimal indemnity function depends on the first and second order conditional expectations of the random recovery rate. The methodology and results in this paper complement the literature regarding the optimal insurance subject to the default risk and provide new insights on problems of similar types. Moreover, we also apply the techniques in this paper to the case of additive background risk, which yields an alternative proof of the main result of Chi and Tan (2021).

Keywords: Optimal insurance, mean-variance optimization, background risk, marginal indemnity function

JEL Classification: C70, G22

Suggested Citation

Boonen, Tim J. and Jiang, Wenjun, Mean-Variance Insurance Design with Counterparty Risk and Incentive Compatibility (February 3, 2022). ASTIN Bulletin, 2022, Available at SSRN: https://ssrn.com/abstract=3894050 or http://dx.doi.org/10.2139/ssrn.3894050

Tim J. Boonen

University of Hong Kong ( email )

Pokfulam Road
Hong Kong
China

Wenjun Jiang (Contact Author)

University of Calgary ( email )

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

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