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European Actuarial Journal

, Volume 7, Issue 1, pp 277–296 | Cite as

Skew-elliptical distributions with applications in risk theory

  • Tomer Shushi
Original Research Paper

Abstract

In this paper we derive important properties of the well-known skew-elliptical (SE) distributions which was introduced in Azzalini and Capitanio (J R Stat Soc Ser B (Stat Methodol) 65:367–389, 2003), and includes the more familiar skew-normal, skew-Student-t and skew-logistic distributions. We then derive the tail value at risk (TVaR) for a portfolio of SE risks. We provide the portfolio risk decomposition with TVaR. Furthermore, we obtain the Esscher premium principle, the weighted-premium principle, and the entropic risk measure with the underlying SE distributions. We also provide an explicit closed-form solution to the optimal portfolio selection with the SE distributions, and provide a numerical simulation of the results.

Keywords

Esscher premium Loss distributions Optimal portfolio selection Skew-elliptical distributions Tail value at risk 

Notes

Acknowledgements

I thank the anonymous referees for their very useful comments.

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Copyright information

© EAJ Association 2017

Authors and Affiliations

  1. 1.Ben-Gurion University of the NegevBeershebaIsrael

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