The problem of risk portfolio optimization with translation-invariant and positive-homogeneous risk measures, which includes value-at-risk (VaR) and tail conditional expectation (TCE), leads to the problem of minimizing a combination of a linear functional and a square root of a quadratic...

This paper introduces a multivariate tail covariance (MTCov) measure, which is a matrix-valued risk measure designed to explore the tail dispersion of multivariate loss distributions. The MTCov is the second multivariate tail conditional moment around the MTCE, the multivariate tail conditional...

This paper introduces a new family of Generalized Hyper-Elliptical (GHE) distributions providing further generalization of the generalized hyperbolic (GH) family of distributions, considered in Ignatieva and Landsman. The GHE family is constructed by mixing a Generalized Inverse Gaussian (GIG)...

This paper deals with the estimation of loss severity distribution arising from the historical data on univariate and multivariate losses. We present an innovative theoretical framework where the closed-form expression for the tail conditional expectation (TCE) is derived for the skewed general...