  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.
