Optimal insurance under rank‐dependent utility and incentive compatibility

Bernard, He, Yan, and Zhou (Mathematical Finance, 25(1), 154–186) studied an optimal insurance design problem where an individual's preference is of the rank‐dependent utility (RDU) type, and show that in general an optimal contract covers both large and small losses. However, their results suf...

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Bibliographic Details
Published in:Mathematical finance 2019-04, Vol.29 (2), p.659-692
Main Authors: Xu, Zuo Quan, Zhou, Xun Yu, Zhuang, Sheng Chao
Format: Article
Language:English
Subjects:
Calculus of variations
Compatibility
Economic models
Finance
incentive compatibility
Incentives
Indemnity
indemnity function
Insurance
Moral dilemmas
Moral hazard
optimal insurance design
probability weighting function
quantile formulation
rank‐dependent utility theory
retention function
Setbacks
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Summary:Bernard, He, Yan, and Zhou (Mathematical Finance, 25(1), 154–186) studied an optimal insurance design problem where an individual's preference is of the rank‐dependent utility (RDU) type, and show that in general an optimal contract covers both large and small losses. However, their results suffer from the unrealistic assumption that the random loss has no atom, as well as a problem of moral hazard that provides incentives for the insured to falsely report the actual loss. This paper addresses these setbacks by removing the nonatomic assumption, and by exogenously imposing the “incentive compatibility” constraint that both indemnity function and insured's retention function are increasing with respect to the loss. We characterize the optimal solutions via calculus of variations, and then apply the result to obtain explicitly expressed contracts for problems with Yaari's dual criterion and general RDU. Finally, we use numerical examples to compare the results between ours and Bernard et al.
ISSN:0960-1627
1467-9965
DOI:10.1111/mafi.12185