Advances in Decision Sciences
Volume 2012 (2012), Article ID 341476, 13 pages
Research Article

A Simulation Approach to Statistical Estimation of Multiperiod Optimal Portfolios

The Jikei University School of Medicine, Tokyo 1828570, Japan

Received 24 February 2012; Accepted 9 April 2012

Academic Editor: Kenichiro Tamaki

Copyright © 2012 Hiroshi Shiraishi. 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.


This paper discusses a simulation-based method for solving discrete-time multiperiod portfolio choice problems under AR(1) process. The method is applicable even if the distributions of return processes are unknown. We first generate simulation sample paths of the random returns by using AR bootstrap. Then, for each sample path and each investment time, we obtain an optimal portfolio estimator, which optimizes a constant relative risk aversion (CRRA) utility function. When an investor considers an optimal investment strategy with portfolio rebalancing, it is convenient to introduce a value function. The most important difference between single-period portfolio choice problems and multiperiod ones is that the value function is time dependent. Our method takes care of the time dependency by using bootstrapped sample paths. Numerical studies are provided to examine the validity of our method. The result shows the necessity to take care of the time dependency of the value function.