Multiple Risks and Uncertain Portfolio Management

This paper studies comparative static effects under uncertainty when investors face a portfolio decision problem with both an endogenous risk and a background risk. Since the security market is complex, there exists situation where security return and background asset return are given by experts’ estimates when they cannot be reflected by historical data. Focusing on such a situation, an uncertain mean-chance model with background risk for optimal portfolio selection is developed, in which the use of chance of portfolio return failing to reach the threshold can help investors easily determine their tolerance toward risk and thus facilitate a decision making. Then we analyze the solution of the programming problem under different threshold return level, i.e., how different degrees of threshold return will affect allocation between risky asset and risk-free asset. Furthermore, we discuss the effects of changes in mean and standard deviation of risky asset and background asset on investment decisions when security return and background asset return follow normal uncertainty distributions. Finally, a real portfolio selection example is given as illustration.