Title: A novel multi-elliptical family of distributions: Definitions, properties and risk capital decomposition
Authors: Zinoviy Landsman - University of Haifa (Israel) [presenting]
Tomer Shushi - Ben Gurion University of the Negev (Israel)
Abstract: The multivariate elliptical family of distributions is well studied and commonly used in actuarial science and finance. However, it has an essential shortcoming: all its univariate marginal distributions are the same, up to location and scale transformations. This happens because these marginal distributions have the same density generator. For example, all marginals of the multivariate Student-t distribution, an important member of the elliptical class, have the same number of degree of freedoms. We introduce a generalization of the multivariate elliptical family of distributions that considers marginals with different density generators. This becomes important when dealing with insurance and financial data. We further provide the main characteristics of the multi-elliptical family of distributions: characteristic and density functions, expectations and covariance matrices. Furthermore, we derive important risk measures for the introduced distributions, such as the value at risk (VaR) and tail conditional expectation (TCE). We also provide the TCE-based capital allocation of aggregate risks.