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http://hdl.handle.net/10397/74794
Title: | Optimal insurance design with a bonus | Authors: | Li, Y Xu, ZQ |
Issue Date: | Nov-2017 | Source: | Insurance : mathematics and economics, Nov. 2017, v. 77, p. 111-118 | Abstract: | This paper investigates an insurance design problem, in which a bonus will be given to the insured if no claim has been made during the whole lifetime of the contract, for an expected utility insured. In this problem, the insured has to consider the so-called optimal action rather than the contracted compensation (or indemnity) due to the existence of the bonus. For any pre-agreed bonus, the optimal insurance contract is given explicitly and shown to be either the full coverage contract when the insured pays high enough premium, or a deductible one otherwise. The optimal contract and bonus are also derived explicitly if the insured is allowed to choose both of them. The contract turns out to be of either zero reward or zero deductible. In all cases, the optimal contracts are universal, that is, they do not depend on the specific form of the utility of the insured. A numerical example is also provided to illustrate the main theoretical results of the paper. | Keywords: | Bonus–malus system Expected utility Insurance contract with bonus Optimal insurance design Personalized contract |
Publisher: | Elsevier | Journal: | Insurance : mathematics and economics | EISSN: | 0167-6687 | DOI: | 10.1016/j.insmatheco.2017.09.003 | Rights: | ©2017 Elsevier B.V. All rights reserved. © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ The following publication Li, Y., & Xu, Z. Q. (2017). Optimal insurance design with a bonus. Insurance: Mathematics and Economics, 77, 111-118 is available at https://dx.doi.org/10.1016/j.insmatheco.2017.09.003 |
Appears in Collections: | Journal/Magazine Article |
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