A new Chance–Variance optimization criterion for portfolio selection in uncertain decision systems

The Markowitz’s mean–variance (M–V) model has received widespread acceptance as a practical tool for portfolio optimization, and his seminal work has been widely extended in the literature. The aim of this article is to extend the M–V method in hybrid decision systems. We suggest a new Chance–Variance (C–V) criterion to model the returns characterized by fuzzy random variables. For this purpose, we develop two types of C–V models for portfolio selection problems in hybrid uncertain decision systems. Type I C–V model is to minimize the variance of total expected return rate subject to chance constraint; while type II C–V model is to maximize the chance of achieving a prescribed return level subject to variance constraint. Hence the two types of C–V models reflect investors’ different attitudes toward risk. The issues about the computation of variance and chance distribution are considered. For general fuzzy random returns, we suggest an approximation method of computing variance and chance distribution so that C–V models can be turned into their approximating models. When the returns are characterized by trapezoidal fuzzy random variables, we employ the variance and chance distribution formulas to turn C–V models into their equivalent stochastic programming problems. Since the equivalent stochastic programming problems include a number of probability distribution functions in their objective and constraint functions, conventional solution methods cannot be used to solve them directly. In this paper, we design a heuristic algorithm to solve them. The developed algorithm combines Monte Carlo (MC) method and particle swarm optimization (PSO) algorithm, in which MC method is used to compute probability distribution functions, and PSO algorithm is used to solve stochastic programming problems. Finally, we present one portfolio selection problem to demonstrate the developed modeling ideas and the effectiveness of the designed algorithm. We also compare the proposed C–V method with M–V one for our portfolio selection problem via numerical experiments.

► A new Chance–Variance criterion is proposed in uncertain decision system. ► Two new types of C–V models for portfolio selection problems are developed. ► An approximation method for general C–V models is discussed. ► The equivalent stochastic programming problems of C–V models are established. ► A heuristic algorithm is designed for solving the equivalent stochastic programming problems.