Portfolio management with background risk under uncertain mean-variance utility

Abstract

This paper studies comparative static effects in a portfolio selection problem when the investor has mean-variance preferences. Since the security market is complex, there exists the situation where security returns are given by experts’ estimates when they cannot be reflected by historical data. This paper discusses the problem in such a situation. Based on uncertainty theory, the paper first establishes an uncertain mean-variance utility model, in which security returns and background asset returns are uncertain variables and subject to normal uncertainty distributions. Then, the effects of changes in mean and standard deviation of uncertain background asset on capital allocation are discussed. Furthermore, the influence of initial proportion in background asset on portfolio investment decisions is analyzed when investors have quadratic mean-variance utility function. Finally, the economic analysis illustration of investment strategy is presented.