On quadratic forms in multivariate generalized hyperbolic random vectors
本文推导了多元广义双曲分布下二次型尾概率和部分矩的精确与近似表达式，并应用于两阶段最小二乘估计量分布和二次型投资组合的预期亏损计算。
Summary This article presents exact and approximate expressions for tail probabilities and partial moments of quadratic forms in multivariate generalized hyperbolic random vectors. The derivations involve a generalization of the classic inversion formula for distribution functions (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.