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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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  • Bernardi, Mauro, 2012. "Risk measures for Skew Normal mixtures," MPRA Paper 39828, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:39828
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    References listed on IDEAS

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    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. 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. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    4. 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.
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    Citations

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    Cited by:

    1. Bernardi, Mauro & Maruotti, Antonello & Petrella, Lea, 2017. "Multiple risk measures for multivariate dynamic heavy–tailed models," Journal of Empirical Finance, Elsevier, vol. 43(C), pages 1-32.
    2. 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.
    3. Markus Haas, 2012. "A Note on the Moments of the Skew-Normal Distribution," Economics Bulletin, AccessEcon, vol. 32(4), pages 3306-3312.
    4. Shi, Yue & Punzo, Antonio & Otneim, Håkon & Maruotti, Antonello, 2023. "Hidden semi-Markov models for rainfall-related insurance claims," Discussion Papers 2023/17, Norwegian School of Economics, Department of Business and Management Science.
    5. Jiang, Chun-Fu & Peng, Hong-Yi & Yang, Yu-Kuan, 2016. "Tail variance of portfolio under generalized Laplace distribution," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 187-203.
    6. Mauro Bernardi & Ghislaine Gayraud & Lea Petrella, 2013. "Bayesian inference for CoVaR," Papers 1306.2834, arXiv.org, revised Nov 2013.
    7. Haas, Markus, 2016. "A note on optimal portfolios under regime–switching," Finance Research Letters, Elsevier, vol. 19(C), pages 209-216.
    8. 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.
    9. Mauro Bernardi & Roy Cerqueti & Arsen Palestini, 2020. "The Skew Normal multivariate risk measurement framework," Computational Management Science, Springer, vol. 17(1), pages 105-119, January.
    10. Paola Stolfi & Mauro Bernardi & Lea Petrella, 2018. "The sparse method of simulated quantiles: An application to portfolio optimization," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 375-398, August.

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    More about this item

    Keywords

    Finite mixtures; Skew Normal distributions; Value-at-Risk; Expected Shortfall probability;
    All these keywords.

    JEL classification:

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

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