Multivariate tail conditional expectation for scale mixtures of skew-normal distribution

Abstract

In practice, a financial or actuarial data set may be a skewed or heavy-tailed and this motivates us to study a class of distribution functions in risk management theory that provide more information about these characteristics resulting in a more accurate risk analysis. In this paper, we consider a multivariate tail conditional expectation (MTCE) for multivariate scale mixtures of skew-normal (SMSN) distributions. This class of distributions contains skewed distributions and some members of this class can be used to analyse heavy-tailed data sets. We also provide a closed form for TCE in a univariate skew-normal distribution framework. Numerical examples are also provided for illustration.