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The Skew Normal multivariate risk measurement framework

Author

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  • Mauro Bernardi

    (University of Padova)

  • Roy Cerqueti

    (University of Macerata)

  • Arsen Palestini

    (University of Rome La Sapienza)

Abstract

In this paper, we consider a random vector $$X=\left( X_1,X_2\right) $$X=X1,X2 following a multivariate Skew Normal distribution and we provide an explicit formula for the expected value of X conditioned to the event $$X \le \overline{X}$$X≤X¯, with $$\overline{X} \in \mathbb {R}^2$$X¯∈R2. Such a conditional expectation has an intuitive interpretation in the context of risk measures.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:comgts:v:17:y:2020:i:1:d:10.1007_s10287-019-00350-8
    DOI: 10.1007/s10287-019-00350-8
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    References listed on IDEAS

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    10. Sharon Lee & Geoffrey McLachlan, 2013. "On mixtures of skew normal and skew $$t$$ -distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(3), pages 241-266, September.
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