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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 751846, 12 pages
http://dx.doi.org/10.1155/2013/751846
Research Article

Optimal Investment with Multiple Risky Assets for an Insurer in an Incomplete Market

1School of Science, Tianjin University, Tianjin 300072, China
2Center for Applied Mathematics, Tianjin University, Tianjin 300072, China
3School of Computing and Mathematical Sciences, Auckland University of Technology, Private Bag 92006, Auckland 1142, New Zealand

Received 30 November 2012; Accepted 6 February 2013

Academic Editor: Xiaochen Sun

Copyright © 2013 Hui Zhao 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

This paper studies the optimal investment problem for an insurer in an incomplete market. The insurer's risk process is modeled by a Lévy process and the insurer is supposed to have the option of investing in multiple risky assets whose price processes are described by the standard Black-Scholes model. The insurer aims to maximize the expected utility of terminal wealth. After the market is completed, we obtain the optimal strategies for quadratic utility and constant absolute risk aversion (CARA) utility explicitly via the martingale approach. Finally, computational results are presented for given raw market data.