On quadratic forms in multivariate generalized hyperbolic random vectors

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.

Volume 108, Issue 2, June 2021, Pages 413–424,

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