Finance-Insurance
Time: 11.00 am
Date:11th of June  2026
Room 3001

Alessandra LUATI (Imperial College, UK) “On a nu-class of limit-Gaussian distributions .”

Abstract : We discuss a transformation of a Student-t random variable that arises in the field of robust filtering with score-driven models. As a function of the degrees of freedom parameter of the generating Student-t random variable, here interpreted as a shape parameter, 1<nu<infinity, the density of the transformation specifies a class of sub-Gaussian distributions that include a location-scale transformation of a symmetric Beta when nu=1 and the Gaussian as a limit for nu tending to infinity. In some sense, it can be viewed as a light-tailed counterpart of the Student-t distribution. The density is derived based on its moments, using Mellin integral transforms. Equivalent representations and reparameterisations are considered. A multivariate version is obtained, based on the distribution of the quadratic form of independent limit-Gaussian random variables. Applications are outlined, such as optimal robust filtering with score-driven models, an area that motivated the derivation of the density, and volatility modelling.