Random fuzzy mean-absolute deviation models for portfolio optimization problem with hybrid uncertainty

Abstract

Absolute deviation is a commonly used risk measure, which has attracted more attentions in portfolio optimization. The existing mean-absolute deviation models are devoted to either stochastic portfolio optimization or fuzzy one. However, practical investment decision problems often involve the mixture of randomness and fuzziness such as stochastic returns with fuzzy information. Thus it is necessary to model portfolio selection problem in such a hybrid uncertain environment. In this paper, we employ random fuzzy variable to describe the stochastic return on individual security with ambiguous information. We first define the absolute deviation of random fuzzy variable and then employ it as risk measure to formulate mean-absolute deviation portfolio optimization models. To find the optimal portfolio, we design random fuzzy simulation and simulation-based genetic algorithm to solve the proposed models. Finally, a numerical example for synthetic data is presented to illustrate the validity of the method.