An Actuarial Index of the Right-Tail Risk

A common characteristic for many insurance risks is the right-tail risk, representing low-frequency, large-loss events. In this paper I propose a measure of the right-tail risk by defining the right-tail deviation and the right-tail index. I explain how the right-tail deviation measures the right-tail risk and compare it to traditional measures such as standard deviation, the Gini mean, and the expected policyholder deficit. The right-tail index is applied to some common parametric families of loss distributions.