Behavioral optimal insurance |
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Authors: | K.C.J. Sung S.C.P. Yam S.P. Yung J.H. Zhou |
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Affiliation: | aDepartment of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong;bDepartment of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong |
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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. |
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Keywords: | Optimal insurance Behavioral finance Cumulative prospect theory Non-convex optimization Generalized insurance layer |
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