Modelling random vectors of dependent risks with different elliptical components

Zinoviy Landsman, Tomer Shushi

Research output: Contribution to journalArticlepeer-review


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.

Original languageAmerican English
Pages (from-to)6-24
Number of pages19
JournalAnnals of Actuarial Science
Issue number1
StatePublished - 22 Mar 2022


  • Elliptical distributions
  • Multi-spherical distributions
  • Risk measures
  • Spherical distributions
  • Tail value at risk
  • Value at risk

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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