Optimal insurance design with a bonus |
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| Affiliation: | 1. School of Economics and Management, Beijing University of Technology, Beijing 100124, China;2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong;1. Department of Mathematics, Division of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Samos, 83200, Greece;2. Faculty of Actuarial Science and Insurance, Sir John Cass Business School, City University London, 106 Bunhill Row, London EC1Y8TZ, UK;1. Maastricht University, Netherlands;2. Tilburg University, Netherlands;3. APG, Netherlands;4. Netspar, Netherlands;5. Kleynen Consultants, Netherlands;1. School of Mathematics and Informational Science, Yantai University, Yantai 264005, China;2. Department of Mathematics, Anhui Normal University, Wuhu 241000, China |
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| 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. |
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| Keywords: | Optimal insurance design Bonus–malus system Insurance contract with bonus Personalized contract Expected utility |
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