Portfolio management using partially observable Markov decision process

Abstract

Portfolio theory is concerned with how an investor should divide his wealth among different securities. This problem was first formulated by Markowitz in 1952. Since then, other more sophisticated formulations have been introduced. However, practical issues like transactions costs and their effects on the portfolio choice in multiple stages have not been widely considered. In our work, we show that the portfolio management problem is appropriately formulated as a Partially Observable Markov Decision Process. We use a Monte Carlo method called "rollout" to approximate an optimal strategy for making decisions. To capture the behavior of stock prices over time, we use two well known models.