Mean-CVaR Portfolio Optimization Models based on Chance Theory

The indeterminacy of financial markets leads investors to face different types of security returns. Usually, security returns are assumed to be random variables when sufficient transaction data are available. If data are missing, they can be regarded as uncertain variables. However, uncertainty and randomness coexist. In this situation, chance theory is the main tool to deal with this complex phenomenon. This paper investigates the conditional value at risk (CVaR) of uncertain random variables and its application to portfolio selection. First, we define the CVaR of uncertain random variables and discuss some of its mathematical properties. Then, we propose an uncertain random simulation to approximate the CVaR. Next, we define the inverse function of the CVaR of uncertain random variables, as well as a computational procedure. As an application in finance, we establish uncertain random mean-CVaR portfolio selection models. We also perform a numerical example to illustrate the applicability of the proposed models. Finally, we numerically compare the mean-CVaR models with the mean-variance models with respect to the optimal investment strategy.