Tail risk estimation based on extreme Lp-quantiles
Abstract
The notion 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 can be embedded in themore general class of Lp-quantiles as the minimizers of an asymmetric power loss function. In this talk, we develop new methods for estimating high Lp-quantiles in the domain of attraction of heavy-tailed distributions