Abstract : Value-at-risk, Conditional Tail Expectation, Conditional Tail Variance and Conditional Tail Moment are classical risk measures. In statistical terms,
the Value-at-risk is the upper a-quantile of the loss distribution where alpha in (0;1) is the confidence level. Here, we focus on the properties of these
risk measures for extreme losses (where alpha tends to zero and is thus no longer fixed). To assign probabilities to extreme losses we assume that the distribution satisfies a von-Mises condition which allows us to work in the general setting, whether the extreme-value index is positive, negative or zero i.e. for all domains of attraction. We also consider these risk measures in the presence of a covariate. The main goal is to propose estimators of the above risk measures for all domains of attraction, for extreme losses, and to include a covariate in the estimation. The estimation method thus combines nonparametric kernel methods with extreme-value statistics. The asymptotic distribution of our estimators is established and their finite sample behavior is illustrated on simulated data and also on a motivating application in the reliability of nuclear reactors.