Risk measures for Skew Normal mixtures
Finite mixtures of Skew distributions have become increasingly popular in the last few years as a flexible tool for handling data displaying several different characteristics such as multimodality, asymmetry and fat-tails. Examples of such data can be found in financial and actuarial applications as well as biological and epidemiological analysis. In this paper we will show that a convex linear combination of multivariate Skew Normal mixtures can be represented as finite mixtures of univariate Skew Normal distributions. This result can be useful in modeling portfolio returns where the evaluation of extremal events is of great interest. We provide analytical formula for different risk measures like the Value-at-Risk and the Expected Shortfall probability.
|Date of creation:||2012|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Haas Markus, 2010. "Skew-Normal Mixture and Markov-Switching GARCH Processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-56, September.
- A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
- Acerbi, Carlo & Tasche, Dirk, 2002.
"On the coherence of expected shortfall,"
Journal of Banking & Finance,
Elsevier, vol. 26(7), pages 1487-1503, July.
- Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
- Bernardi, Mauro & Maruotti, Antonello & Petrella, Lea, 2012. "Skew mixture models for loss distributions: A Bayesian approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 617-623.
- Bernardi, Mauro & Maruotti, Antonello & Lea, Petrella, 2012. "Skew mixture models for loss distributions: a Bayesian approach," MPRA Paper 39826, University Library of Munich, Germany.