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Risk measures for skew normal mixtures

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Author Info

  • Bernardi, Mauro

Abstract

In this paper we show that linear combinations of multivariate skew normal mixtures can be represented as finite mixtures of univariate skew normals. Based on this result we provide an analytical formula for some well known risk measures.

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Bibliographic Info

Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 83 (2013)
Issue (Month): 8 ()
Pages: 1819-1824

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Handle: RePEc:eee:stapro:v:83:y:2013:i:8:p:1819-1824

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Related research

Keywords: Finite mixtures; Skew normal distributions; Risk measures; Value-at-Risk; Expected shortfall;

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References

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  1. 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.
  2. 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.
  3. 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.
  4. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
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Cited by:
  1. Markus Haas, 2012. "A Note on the Moments of the Skew-Normal Distribution," Economics Bulletin, AccessEcon, vol. 32(4), pages 3306-3312.
  2. 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.
  3. Mauro Bernardi & Ghislaine Gayraud & Lea Petrella, 2013. "Bayesian inference for CoVaR," Papers 1306.2834, arXiv.org, revised Nov 2013.

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