Risk measures for Skew Normal mixtures
AbstractFinite 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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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 39828.
Date of creation: 2012
Date of revision:
Finite mixtures; Skew Normal distributions; Value-at-Risk; Expected Shortfall probability;
Find related papers by JEL classification:
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-07-14 (All new papers)
- NEP-BAN-2012-07-14 (Banking)
- NEP-ECM-2012-07-14 (Econometrics)
- NEP-RMG-2012-07-14 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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- 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.
- Bernardi, Mauro & Maruotti, Antonello & Lea, Petrella, 2012. "Skew mixture models for loss distributions: a Bayesian approach," MPRA Paper 39826, University Library of Munich, Germany.
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- Mauro Bernardi & Ghislaine Gayraud & Lea Petrella, 2013. "Bayesian inference for CoVaR," Papers 1306.2834, arXiv.org, revised Nov 2013.
- Bernardi, Mauro & Maruotti, Antonello & Lea, Petrella, 2012.
"Skew mixture models for loss distributions: a Bayesian approach,"
39826, University Library of Munich, Germany.
- 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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