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Risk measures for Skew Normal mixtures

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  • Bernardi, Mauro

Abstract

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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 39828.

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Date of creation: 2012
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Handle: RePEc:pra:mprapa:39828

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Keywords: Finite mixtures; Skew Normal distributions; Value-at-Risk; Expected Shortfall probability;

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References

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  1. Bernardi, Mauro & Maruotti, Antonello & Lea, Petrella, 2012. "Skew mixture models for loss distributions: a Bayesian approach," MPRA Paper 39826, University Library of Munich, Germany.
  2. 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.
  3. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
  4. 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.
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Cited by:
  1. Bernardi, Mauro & Maruotti, Antonello & Lea, Petrella, 2012. "Skew mixture models for loss distributions: a Bayesian approach," MPRA Paper 39826, University Library of Munich, Germany.
  2. Markus Haas, 2012. "A Note on the Moments of the Skew-Normal Distribution," Economics Bulletin, AccessEcon, vol. 32(4), pages 3306-3312.
  3. Mauro Bernardi & Ghislaine Gayraud & Lea Petrella, 2013. "Bayesian inference for CoVaR," Papers 1306.2834, arXiv.org, revised Nov 2013.

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