A risk index model for uncertain portfolio selection with background risk

Abstract

Abstract This study proposes a new uncertain risk index model with background risk and presents its deterministic equivalents. The security returns and background asset returns are assumed as uncertain variables and estimated by experts. To discuss the influence of background risk on investment decisions, we compare the proposed model with a variant without background risk and find that the portfolio with background risk produces an equal or lower return than the one without background risk. The effects of changes in the standard deviation of background asset and the risk-free interest rate on optimal expected value are discussed. Two different risk measures for portfolio optimization model with background risk are compared, viz., the risk index model with background risk is further compared with the mean chance model with background risk. The nonlinear risk index model is solved by using a genetic algorithm. The efficiency of the genetic algorithm and the applications of the proposed models are illustrated through numerical experiments.