Multivariate doubly truncated moments for generalized skew-elliptical distributions with application to multivariate tail conditional risk measures

TL;DR

This paper derives explicit formulas for multivariate doubly truncated moments of generalized skew-elliptical distributions, including applications to tail risk measures like MTCE and MTCov, covering many useful distribution families.

Contribution

It provides new explicit expressions for truncated moments of GSE distributions and applies them to multivariate tail risk measures, extending previous work.

Findings

Explicit formulas for truncated moments of GSE distributions

Application to multivariate tail conditional expectation and covariance

Coverage of various skew-elliptical distribution families

Abstract

In this paper, we focus on multivariate doubly truncated first two moments of generalized skew-elliptical (GSE) distributions and derive explicit expressions for them. It includes many useful distributions, for examples, generalized skew-normal (GSN), generalized skew-Laplace (GSLa), generalized skew-logistic (GSLo) and generalized skew student-$t$ (GSSt) distributions, all as special cases. We also give formulas of multivariate doubly truncated expectation and covariance for GSE distributions. As applications, we show the results of multivariate tail conditional expectation (MTCE) and multivariate tail covariance (MTCov) for GSE distributions.