Actuarial Seminar: Prof. Antoine Usseglio Carleve (University of Avignon)

Abstract: The expectile and Expected Shortfall are prime candidates for being standard risk measures in actuarial and financial contexts, for their ability to recover information about probabilities and typical behavior of extreme values, as well as their axiomatic properties. A series of recent papers has focused on their estimation at extreme levels and has obtained the asymptotic normality of the proposed estimators. The obtention of accurate confidence intervals for extreme expectiles and Expected Shortfall is paramount in any decision process in which they are involved, but actual inference on these tail risk measures is still a difficult question due to their sensitivity to tail heaviness. This talk focuses on asymptotic Gaussian inference about tail expectiles in the challenging context of heavy-tailed observations, and tail Expected Shortfall in the general max-domain of attraction. We use an in-depth analysis of the proofs of asymptotic normality results to derive bias-reduced and variance-corrected Gaussian confidence intervals. We illustrate the usefulness of our construction on several sets of financial and insurance claims data.

Seminar organized by Prof. E. Hashorva