Stochastic Linear Programming Approach for Portfolio Optimization Problem

Abstract

There is no doubt that portfolio selection problems play an important role in finance, which recommend valuable choices among various investment strategies. In our study, we consider the portfolio optimization problem as a stochastic linear programming problem. By transforming the stochastic programming problem to deterministic problems by applying the probability models, we establish the variant of Markowitz model, which is related to Sharpe ratios. Then the portfolio selection problem is transferred to an optimization problem over the efficient solution set of bi-objective programming problems. This equivalent problem is solved by a multi-objective evolutionary algorithm with less time consumption due to the population approach. An experiment on Vietnam stock market data will be implemented and gives detailed analysis about trade-off of objective functions.