Behavioral optimal insurance

K.C.J. Sung, S.C.P. Yam, S.P. Yung and J.H. Zhou

Insurance: Mathematics and Economics, 2011, vol. 49, issue 3, 418-428

Abstract: The present work studies the optimal insurance policy offered by an insurer adopting a proportional premium principle to an insured whose decision-making behavior is modeled by Kahneman and Tversky’s Cumulative Prospect Theory with convex probability distortions. We show that, under a fixed premium rate, the optimal insurance policy is a generalized insurance layer (that is, either an insurance layer or a stop–loss insurance). This optimal insurance decision problem is resolved by first converting it into three different sub-problems similar to those in Jin and Zhou (2008); however, as we now demand a more regular optimal solution, a completely different approach has been developed to tackle them. When the premium is regarded as a decision variable and there is no risk loading, the optimal indemnity schedule in this form has no deductibles but a cap; further results also suggests that the deductible amount will be reduced if the risk loading is decreased. As a whole, our paper provides a theoretical explanation for the popularity of limited coverage insurance policies in the market as observed by many socio-economists, which serves as a mathematical bridge between behavioral finance and actuarial science.

Keywords: Optimal insurance; Behavioral finance; Cumulative prospect theory; Non-convex optimization; Generalized insurance layer (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (21)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:49:y:2011:i:3:p:418-428

DOI: 10.1016/j.insmatheco.2011.04.008

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