The Multi-period Portfolio Optimization Using Possibilistic Entropy and Particle Swarm Optimization(PSO)

Abstract

In this research, multi-period stock portfolio selection was modeled and solved under uncertainty and considering transaction costs. A possibilistic mean-semivariance-entropy model for multi-period portfolio selection by taking into account four criteria viz., return, risk, diversification degree of portfolio and transaction cost was introduced. In this model, the return level by the possibilistic mean value of return, the risk level by the lower possibilistic semivariance of return, and the diversification degree of portfolio was quantified by the possibilistic entropy. We used fuzzy theory in order to consider uncertainty in proposed model and considered asset returns as trapezoidal fuzzy numbers. MOPSO algorithm was used to solve the model. In order to evaluate the proposed models performance, a similar model including proportional entropy was modeled and solved and its results were compared with the possibilistic entropy model. The results of this comparison showed that the possibilistic entropy model is better than the proportional entropy model because it provides better efficiency frontier. Regarding the optimized portfolios in one-time implementation of the algorithm on the possibilistic entropy model in third-time period, the highest percentage of stocks selected in the optimal portfolio of risk seeker, risk averse and risk neutral investor is respectively kagol,hakeshti and shekhark.

Keywords

• multi-period portfolio
• multi objective particle swarm optimization (mopso)
• possibilistic entropy
• proportional entropy
• terminal wealth