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Modelling random vectors of dependent risks with different elliptical components

Published online by Cambridge University Press:  22 February 2021

Zinoviy Landsman  and
Tomer Shushi
Zinoviy Landsman
Affiliation:
Actuarial Research Center, Department of Statistics, University of Haifa, Haifa3498838, Israel Holon Institute of Technology, Holon5810201, Israel
Tomer Shushi*
Affiliation:
Department of Business Administration, Guilford Glazer Faculty of Business and Management, Ben-Gurion University of the Negev, Beer-Sheva8410501, Israel
*
*Corresponding author. E-mail: tomershu@bgu.ac.il
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Abstract

In Finance and Actuarial Science, the multivariate elliptical family of distributions is a famous and well-used model for continuous risks. However, it has an essential shortcoming: all its univariate marginal distributions are the same, up to location and scale transformations. For example, all marginals of the multivariate Student’s t-distribution, an important member of the elliptical family, have the same number of degrees of freedom. We introduce a new approach to generate a multivariate distribution whose marginals are elliptical random variables, while in general, each of the risks has different elliptical distribution, which is important when dealing with insurance and financial data. The proposal is an alternative to the elliptical copula distribution where, in many cases, it is very difficult to calculate its risk measures and risk capital allocation. We study the main characteristics of the proposed model: characteristic and density functions, expectations, covariance matrices and expectation of the linear regression vector. We calculate important risk measures for the introduced distributions, such as the value at risk and tail value at risk, and the risk capital allocation of the aggregated risks.

Keywords

Elliptical distributionsSpherical distributionsMulti-spherical distributionsRisk measuresTail value at riskValue at risk
Type
Original Research Paper
Information
Annals of Actuarial Science , Volume 16 , Issue 1 , March 2022 , pp. 6 - 24
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

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