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Journal of Applied Mathematics
Volume 2015, Article ID 186061, 18 pages
http://dx.doi.org/10.1155/2015/186061
Research Article

The Optimal Insurance Policy for the General Fixed Cost of Handling an Indemnity under Rank-Dependent Expected Utility

College of Economics and Management, Hunan Normal University, Changsha 410081, China

Received 20 July 2015; Revised 21 October 2015; Accepted 22 October 2015

Academic Editor: Walter Briec

Copyright © 2015 Liurui Deng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Based on Bernard et al.’s research, we focus on the Pareto optimal insurance design with the insured’s Rank-Dependent Expected Utility (RDEU). Compared with their previous work, our novelties are the more general fixed cost function of the insurer and the discussion of adverse selection and moral hazard. In particular, Bernard et al. only consider the case in which the fixed cost function of handling an indemnity is the linear function. However, the fixed cost function is not just linear functions in real insurance market. So, we explore the more general fixed cost function including both the linear and nonlinear functions. On the other hand, we consider adverse selection and moral hazard which are involved by Bernard et al. Leading adverse selection and moral hazard into our research makes our results more practical and meaningful. Moreover, we provide an insight into the sensitivity of an optimal solution for the insured’s initial wealth and the parameters related to the fixed cost function of handling an indemnity. We further compare the two different utility functions of the insured in terms of influence of optimal policy analysis.