Estimating the Conditional Tail Expectation of Randomly Right-Censored Heavy-Tailed Data

The conditional tail expectation (CTE) is a very useful tool in risk management and one of the best-known risk measures in the realm of insurance. This paper focuses on the estimation of the CTE of data that are heavy-tailed and randomly censored to the right while the existing works are based on complete datasets. By applying survival and extreme value theories, we define an estimator to the CTE and we establish its asymptotic normality. This estimation procedure is evaluated through a simulation study and applied to two real datasets of insurance losses and Aids survival time.