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Multivariate elliptical truncated moments


Arismendi, Juan C; Broda, Simon (2017). Multivariate elliptical truncated moments. Journal of Multivariate Analysis, 157:29-44.

Abstract

In this study, we derive analytic expressions for the elliptical truncated moment generating function (MGF), the zeroth-, first-, and second-order moments of quadratic forms of the multivariate normal, Student’s , and generalized hyperbolic distributions. The resulting formulas were tested in a numerical application to calculate an analytic expression of the expected shortfall of quadratic portfolios with the benefit that moment based sensitivity measures can be derived from the analytic expression. The convergence rate of the analytic expression is fast–one iteration–for small closed integration domains, and slower for open integration domains when compared to the Monte Carlo integration method. The analytic formulas provide a theoretical framework for calculations in robust estimation, robust regression, outlier detection, design of experiments, and stochastic extensions of deterministic elliptical curves results.

Abstract

In this study, we derive analytic expressions for the elliptical truncated moment generating function (MGF), the zeroth-, first-, and second-order moments of quadratic forms of the multivariate normal, Student’s , and generalized hyperbolic distributions. The resulting formulas were tested in a numerical application to calculate an analytic expression of the expected shortfall of quadratic portfolios with the benefit that moment based sensitivity measures can be derived from the analytic expression. The convergence rate of the analytic expression is fast–one iteration–for small closed integration domains, and slower for open integration domains when compared to the Monte Carlo integration method. The analytic formulas provide a theoretical framework for calculations in robust estimation, robust regression, outlier detection, design of experiments, and stochastic extensions of deterministic elliptical curves results.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Physical Sciences > Numerical Analysis
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Scope:Discipline-based scholarship (basic research)
Language:English
Date:May 2017
Deposited On:21 Aug 2023 10:57
Last Modified:29 Jun 2024 01:38
Publisher:Elsevier
ISSN:0047-259X
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.jmva.2017.02.011
Other Identification Number:merlin-id:16240
  • Content: Published Version
  • Language: English
  • Publisher License