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Risk measures for skew normal mixtures

Author

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  • 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.

Suggested Citation

  • Bernardi, Mauro, 2013. "Risk measures for skew normal mixtures," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1819-1824.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:8:p:1819-1824
    DOI: 10.1016/j.spl.2013.04.016
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    References listed on IDEAS

    as
    1. 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.
    2. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. repec:eee:apmaco:v:282:y:2016:i:c:p:187-203 is not listed on IDEAS
    2. Mauro Bernardi & Ghislaine Gayraud & Lea Petrella, 2013. "Bayesian inference for CoVaR," Papers 1306.2834, arXiv.org, revised Nov 2013.
    3. repec:eee:empfin:v:43:y:2017:i:c:p:1-32 is not listed on IDEAS
    4. Haas, Markus, 2016. "A note on optimal portfolios under regime–switching," Finance Research Letters, Elsevier, vol. 19(C), pages 209-216.
    5. 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.
    6. Bernardi Mauro & Roy Cerqueti & Arsen Palestini, 2016. "Allocation of risk capital in a cost cooperative game induced by a modified Expected Shortfall," Papers 1608.02365, arXiv.org.
    7. Markus Haas, 2012. "A Note on the Moments of the Skew-Normal Distribution," Economics Bulletin, AccessEcon, vol. 32(4), pages 3306-3312.

    More about this item

    Keywords

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

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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