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Risk management is very important for individual investors or companies.There are many ways to measure the risk of investment. Prices of risky assetsvary rapidly and randomly due to the complexity of finance market. Randominterval is a good tool to describe uncertainty with both randomness andimprecision. Considering the uncertainty of financial market, we employ randomintervals to describe the returns of a risk asset and consider the tail risk,which is called the interval-valued Conditional Value at Risk (ICVaR, forshort). Such an ICVaR is a risk measure and satisfies subadditivity. Under thenew risk measure ICVaR, as a manner similar to the classical portfolio model ofMarkowitz, optimal interval-valued portfolio selection models are built. Basedon the real data from mainland Chinese stock market, the case study shows thatour models are interpretable and consistent with the practical scenarios.

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