2013
DOI: 10.1016/j.spl.2013.04.016
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Risk measures for skew normal mixtures

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 dist… Show more

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Cited by 32 publications
(18 citation statements)
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“…A source of asymmetry different from regime-specific expected returns is within-regime skewness, which can be allowed for, e.g., by replacing the Gaussian in (1) by Azzalini's (1985) skewnormal distribution. This naturally leads to the class of finite mixtures of skew-normal distributions (e.g., Bernardi, 2013;and Otiniano et al, 2015), which nests the class of normal mixtures and may be useful when portfolio return distributions display asymmetries. Stochastic dominance criteria for single-component skew-normal distributions have been investigated by Blasi and Scarlatti (2012).…”
Section: Discussionmentioning
confidence: 99%
“…A source of asymmetry different from regime-specific expected returns is within-regime skewness, which can be allowed for, e.g., by replacing the Gaussian in (1) by Azzalini's (1985) skewnormal distribution. This naturally leads to the class of finite mixtures of skew-normal distributions (e.g., Bernardi, 2013;and Otiniano et al, 2015), which nests the class of normal mixtures and may be useful when portfolio return distributions display asymmetries. Stochastic dominance criteria for single-component skew-normal distributions have been investigated by Blasi and Scarlatti (2012).…”
Section: Discussionmentioning
confidence: 99%
“…see, Nadarajah et al (2014) and Bernardi (2013), while the SCoVaR and SCoES becomesγ τ1|τ2 i| k =i X k ≡ SCoV aR…”
Section: Conclusion and Further Developmentsmentioning
confidence: 99%
“…Due to lack of enough observations the same comparison could not be performed for lower confidence levels. The ES evaluated at the VaR level x is analytically tractable for mixture of Skew-Normal, in fact it is possible to show that it is the weighted average of the Expected Shortfalls of each mixture components (Bernardi, 2012), where…”
Section: Application To Insurance Claim Datamentioning
confidence: 99%