Estimation of extreme expectiles from heavy tailed distributions

International audienceThe class of quantiles lies at the heart of extreme-value theory and is one of the basic tools in risk management. The alternative family of expectiles is based on squared rather than absolute error loss minimization. Both quantiles and expectiles were embedded in the more general class of M-quantiles as the minimizers of a generic asymmetric convex loss function. It has been proved very recently that the only M-quantiles that are coherent risk measures are the expectiles. Least asymmetrically weighted squares estimation of expectiles did not, however, receive yet as much attention as quantile-based risk measures from the perspective of extreme values. We develop new methods for estimating the Value at Risk and Expected Shortfall measures via high expectiles. We focus on the challenging domain of attraction of heavy-tailed distributions that better describe the tail structure and sparseness of most actuarial and financial data