Portfolio selection models based on interval-valued conditional value at risk (ICVaR) and empirical analysis

Risk management is very important for individual investors or companies. There are many ways to measure the risk of investment. Prices of risky assets vary rapidly and randomly due to the complexity of finance market. Random interval is a good tool to describe uncertainty with both randomness and imprecision. Considering the uncertainty of financial market, we employ random intervals to describe the returns of a risk asset and consider the tail risk, which is called the interval-valued Conditional Value at Risk (ICVaR, for short). Such an ICVaR is a risk measure and satisfies subadditivity. Under the new risk measure ICVaR, as a manner similar to the classical portfolio model of Markowitz, optimal interval-valued portfolio selection models are built. Based on the real data from mainland Chinese stock market, the case study shows that our models are interpretable and consistent with the practical scenarios.