Abstract
We present general results on the univariate tail conditional expectation (TCE) and multivariate tail conditional expectation (MTCE) for location-scale mixture of elliptical distributions. Examples include the location-scale mixture of normal distributions, location-scale mixture of Student- 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. More specifically, we give MTCEs of generalized hyperbolic and slash distributions, and discuss the difference of MTCEs for generalized hyperbolic and slash distributions. As an illustrative example, we discuss the MTCE of five stocks including Amazon, Goldman Sachs, IBM, Google and Apple.
Acknowledgements
The authors thank the anonymous referees and the Editor for their helpful comments and suggestions, which have led to the improvement of this paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).