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On quadratic forms in multivariate generalized hyperbolic random vectors
[Expected shortfall: A natural coherent alternative to value at risk]

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  • Simon A Broda
  • Juan Arismendi Zambrano

Abstract

SummaryThis 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.

Suggested Citation

  • Simon A Broda & Juan Arismendi Zambrano, 2021. "On quadratic forms in multivariate generalized hyperbolic random vectors [Expected shortfall: A natural coherent alternative to value at risk]," Biometrika, Biometrika Trust, vol. 108(2), pages 413-424.
    • Handle: RePEc:oup:biomet:v:108:y:2021:i:2:p:413-424.
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