Stein’s lemma for truncated generalized skew-elliptical random vectors

Abstract

Inspired by Shushi [1] and Adcock et al. [2], we consider Stein’s lemma for truncated generalized skew-elliptical random vectors. We provide two Stein’s lemmas. One is Stein’s lemma for truncated generalized skew-elliptical random vectors, the other is a special form of Stein’s lemma for truncated generalized skew-elliptical random vectors. Finally, the conditional tail expectation allocation, the lower-orthant conditional tail expectation at probability level q, the upper-orthant conditional tail expectation at probability level q, the truncated version of Wang’s premium, the multivariate tail conditional expectation and the multivariate tail covariance matrix as applications are given.

Keywords

• generalized skew-elliptical distributions
• generalized skew-normal distributions
• truncated random vectors
• stein’s lemma