Stochastic Portfolio Selection Problem with Reliability Criteria

Portfolio selection focuses on allocating the capital to a set of securities such that the profit or the risks can be optimized. Due to the uncertainty of the real‐world life, the return parameters always take uncertain information in the realistic environments because of the scarcity of the a priori knowledge or uncertain disturbances. This paper particularly considers a portfolio selection process in the stochastic environment, where the return parameters are characterized by sample‐based correlated random variables. To decrease the decision risks, three evaluation criteria are proposed to generate the reliable portfolio selection plans, including max‐min reliability criterion, percentile reliability criterion, and expected disutility criterion. The equivalent linear (mixed integer) programming models are also deduced for different evaluation strategies. A genetic algorithm with a polishing strategy is designed to search for the approximate optimal solutions of the proposed models. Finally, a series of numerical experiments are implemented to demonstrate the effectiveness and performance of the proposed approaches.