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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 972487, 13 pages
Research Article

Precommitted Investment Strategy versus Time-Consistent Investment Strategy for a Dual Risk Model

1School of Management, Tianjin University, Tianjin 300072, China
2School of Science, Tianjin University of Science & Technology, Tianjin 300457, China
3School of Science, Tianjin University, Tianjin 300072, China
4College of Economics & Management, Tianjin University of Science Technology, Tianjin 300222, China

Received 23 February 2014; Accepted 30 April 2014; Published 19 May 2014

Academic Editor: Xiang Li

Copyright © 2014 Lidong Zhang 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.


We are concerned with optimal investment strategy for a dual risk model. We assume that the company can invest into a risk-free asset and a risky asset. Short-selling and borrowing money are allowed. Due to lack of iterated-expectation property, the Bellman Optimization Principle does not hold. Thus we investigate the precommitted strategy and time-consistent strategy, respectively. We take three steps to derive the precommitted investment strategy. Furthermore, the time-consistent investment strategy is also obtained by solving the extended Hamilton-Jacobi-Bellman equations. We compare the precommitted strategy with time-consistent strategy and find that these different strategies have different advantages: the former can make value function maximized at the original time and the latter strategy is time-consistent for the whole time horizon. Finally, numerical analysis is presented for our results.