The notion of "tail risk" has been a crucial consideration in modern risk management. To achieve a comprehensive … understanding of the tail risk, we carry out an axiomatic study for risk measures which quantify the tail risk, that is, the … behavior of a risk beyond a certain quantile. Such risk measures are referred to as tail risk measures in this paper. The two …

transform to be a probability distortion. As the first application, we construct new risk measures using distributional … transforms. Sufficient and necessary conditions are given to ensure the convexity or coherence of the generated risk measures. In … the second application, we introduce a new method for sensitivity analysis of risk measures based on composition groups of …