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OPTIMAL INCENTIVE-COMPATIBLE INSURANCE WITH BACKGROUND RISK

Published online by Cambridge University Press:  29 March 2021

Yichun Chi  and
Ken Seng Tan
Yichun Chi*
Affiliation:
China Institute for Actuarial Science Central University of Finance and Economics, Beijing102206, China E-Mail: [email protected]
Ken Seng Tan
Affiliation:
Division of Banking & Finance, Nanyang Business School Nanyang Technological University, Singapore E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

In this paper, the optimal insurance design is studied from the perspective of an insured, who faces an insurable risk and a background risk. For the reduction of ex post moral hazard, alternative insurance contracts are asked to satisfy the principle of indemnity and the incentive-compatible condition. As in the literature, it is assumed that the insurer calculates the insurance premium solely on the basis of the expected indemnity. When the insured has a general mean-variance preference, an explicit form of optimal insurance is derived explicitly. It is found that the stochastic dependence between the background risk and the insurable risk plays a critical role in the insured’s risk transfer decision. In addition, the optimal insurance policy can often change significantly once the incentive-compatible constraint is removed.

Keywords

Background riskconditional expectation functionincentive compatibilitymean-variance preferenceoptimal insurance designD81G22
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 2 , May 2021 , pp. 661 - 688
Copyright
© 2021 by Astin Bulletin. All rights reserved

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