Journal
MATHEMATICAL FINANCE
Volume 25, Issue 1, Pages 154-186Publisher
WILEY
DOI: 10.1111/mafi.12027
Keywords
optimal insurance design; rank-dependent expected utility; inverse-S shaped probability distortion; indemnity; quantile formulation; deductible
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Funding
- Natural Sciences and Engineering Research Council of Canada
- start-up fund at Columbia University
- National Basic Research Program of China (973 Program) [2007CB814902]
- Key Laboratory of Random Complex Structures and Data Science, CAS [2008DP173182]
- Science Fund for Creative Research Groups of NNSF [11021161]
- GRF grant [CUHK419511]
- CUHK
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We consider an optimal insurance design problem for an individual whose preferences are dictated by the rank-dependent expected utility (RDEU) theory with a concave utility function and an inverse-S shaped probability distortion function. This type of RDEU is known to describe human behavior better than the classical expected utility. By applying the technique of quantile formulation, we solve the problem explicitly. We show that the optimal contract not only insures large losses above a deductible but also insures small losses fully. This is consistent, for instance, with the demand for warranties. Finally, we compare our results, analytically and numerically, both to those in the expected utility framework and to cases in which the distortion function is convex or concave.
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