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| Title: | Optimal insurance under rank-dependent utility and incentive compatibility | Authors: | Xu, ZQ Zhou, XY Zhuang, SC |
Issue Date: | Apr-2019 | Source: | Mathematical finance, Apr. 2019, v. 29, no. 2, p.659-692 | Abstract: | 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. | Keywords: | Incentive compatibility Indemnity function Moral hazard Optimal insurance design Probability weighting function Quantile formulation Rank-dependent utility theory Retention function |
Publisher: | Wiley-Blackwell | Journal: | Mathematical finance | ISSN: | 0960-1627 | DOI: | 10.1111/mafi.12185 | Rights: | © 2018 Wiley Periodicals, Inc. This is the peer reviewed version of the following article: Xu, Z. Q., Zhou, X. Y., & Zhuang, S. C. (2019). Optimal insurance under rank‐dependent utility and incentive compatibility. Mathematical Finance, 29(2), 659-692, which has been published in final form at https://doi.org/10.1111/mafi.12185. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited. |
| Appears in Collections: | Journal/Magazine Article |
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| Xu_Optimal_Insurance_Under.pdf | Pre-Published version | 833.29 kB | Adobe PDF | View/Open |
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