Multi-Period Portfolio Optimization Using Dynamic Programming Approach

Portfolio selection has always been one of the important issues in the field of investment management, which discusses how to allocate an investor's capital to different assets and form an efficient portfolio. If the modeling assumptions for portfolio optimization is closer to the real world, the results will be more reliable. Considering single horizon for investment is not real and more investors are investing for more than one period to be able to revise their positions over time. Moreover, in the real world, data and parameters are always uncertain. Therefore, the development of multi-period portfolio optimization models is a basic requirement. In this paper, based on the portfolio theory, a new multi-period portfolio selection model is proposed, which contains transaction costs, liquidity constraints, threshold constraints, cardinality constraints and class constraints. Moreover, mean absolute deviation is used as a measure of risk and uncertainty of data is modeled with scenario tree. Also, in order to solve the proposed model, the dynamic programming method has been used and finally, the model efficiency was tested using data for 5 stocks from Tehran Stock Exchange in a period of 1390 to 1394. In the proposed model, the effect of some factors such as boundary of decision variables and the number of assets in the portfolio is examined. The results indicate that the proposed model has a suitable performance and completely consistent with the theory.