On quadratic forms in multivariate generalized hyperbolic random vectors (Biometrika - Accepted)

Abstract

Exact and approximate expressions for tail probabilities and partial moments of quadratic forms in multivariate generalized hyperbolic random vectors are obtained. The derivations involve a generalization of the classic inversion formula of Gil-Pelaez (1951). Two numerical applications are considered: the distribution of the two stage least squares estimator, and the expected shortfall of a quadratic portfolio.

Link: https://doi.org/10.1093/biomet/asaa067