Conditional tail risk expectations for location-scale mixture of elliptical distributions

TL;DR

This paper derives general formulas for tail conditional expectations in univariate and multivariate settings for location-scale mixtures of elliptical distributions, with applications to portfolio risk analysis.

Contribution

It provides new theoretical results on tail risk expectations for a broad class of mixture distributions, including normal, Student-t, Logistic, and Laplace mixtures.

Findings

Formulas for univariate and multivariate TCE for mixture distributions

Application to portfolio risk decomposition using TCE

Examples include normal, Student-t, Logistic, and Laplace mixtures

Abstract

We present general results on the univariate tail conditional expectation (TCE) and multivariate tail conditional expectation for location-scale mixture of elliptical distributions. Examples include the location-scale mixture of normal distributions, location-scale mixture of Student-$t$ distributions, location-scale mixture of Logistic distributions and location-scale mixture of Laplace distributions. We also consider portfolio risk decomposition with TCE for location-scale mixture of elliptical distributions.