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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 413072, 14 pages
http://dx.doi.org/10.1155/2015/413072
Research Article

Optimal Investment and Consumption for an Insurer with High-Watermark Performance Fee

1School of Mathematics and Computer Science, Anhui Normal University, Wuhu, Anhui 241000, China
2School of Finance, Nanjing University of Finance and Economics, Nanjing, Jiangsu 210023, China

Received 18 August 2015; Accepted 5 October 2015

Academic Editor: Xinguang Zhang

Copyright © 2015 Lin Xu et al. 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

The optimal investment and consumption problem is investigated for an insurance company, which is subject to the payment of high-watermark fee from profit. The objective of insurance company is to maximize the expected cumulated discount utility up to ruin time. The consumption behavior considered in this paper can be viewed as dividend payment of the insurance company. It turns out that the value function of the proposed problem is the viscosity solution to the associated HJB equation. The regularity of the viscosity is discussed and some asymptotic results are provided. With the help of the smooth properties of viscosity solutions, we complete the verification theorem of the optimal control policies and the potential applications of the main result are discussed.