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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 840725, 11 pages
Research Article

A Stochastic Dynamic Programming Approach Based on Bounded Rationality and Application to Dynamic Portfolio Choice

Business School, Central South University, Changsha, Hunan 410083, China

Received 14 March 2014; Accepted 5 May 2014; Published 22 May 2014

Academic Editor: Fenghua Wen

Copyright © 2014 Wenjie Bi 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.


Dynamic portfolio choice is an important problem in finance, but the optimal strategy analysis is difficult when considering multiple stochastic volatility variables such as the stock price, interest rate, and income. Besides, recent research in experimental economics indicates that the agent shows limited attention, considering only the variables with high fluctuations but ignoring those with small ones. By extending the sparse max method, we propose an approach to solve dynamic programming problem with small stochastic volatility and the agent’s bounded rationality. This approach considers the agent’s behavioral factors and avoids effectively the “Curse of Dimensionality” in a dynamic programming problem with more than a few state variables. We then apply it to Merton dynamic portfolio choice model with stochastic volatility and get a tractable solution. Finally, the numerical analysis shows that the bounded rational agent may pay no attention to the varying equity premium and interest rate with small variance.