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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 9693419, 8 pages
http://dx.doi.org/10.1155/2016/9693419
Research Article

Worst-Case Investment and Reinsurance Optimization for an Insurer under Model Uncertainty

1School of Science, Tianjin University, Tianjin 300072, China
2School of Science, Tianjin University of Science & Technology, Tianjin 300457, China
3School of Economics and Management, Tianjin University of Science & Technology, Tianjin 300222, China
4Financial Engineering and Risk Management Research Center, Tianjin University of Science & Technology, Tianjin 300222, China

Received 5 September 2016; Revised 6 November 2016; Accepted 28 November 2016

Academic Editor: Gafurjan Ibragimov

Copyright © 2016 Xiangbo Meng 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

In this paper, we study optimal investment-reinsurance strategies for an insurer who faces model uncertainty. The insurer is allowed to acquire new business and invest into a financial market which consists of one risk-free asset and one risky asset whose price process is modeled by a Geometric Brownian motion. Minimizing the expected quadratic distance of the terminal wealth to a given benchmark under the “worst-case” scenario, we obtain the closed-form expressions of optimal strategies and the corresponding value function by solving the Hamilton-Jacobi-Bellman (HJB) equation. Numerical examples are presented to show the impact of model parameters on the optimal strategies.