Arismendi Zambrano, Juan and Broda, Simon A. (2016) Multivariate Elliptical Truncated Moments. Working Paper. SSRN.

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Abstract

In this study, we derived 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 t, and generalised hyperbolic distributions. The resulting formulae 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 formulae provide a theoretical framework for calculations in robust estimation, robust regression, outlier detection, design of experiments, and stochastic extensions of deterministic elliptical curves results.

Item Type:	Monograph (Working Paper)
Additional Information:	The final published version of this article is available at: Arismendi Zambrano, Juan and Broda, Simon A., Multivariate Elliptical Truncated Moments. Journal of Multivariate Analysis Volume 157, May 2017, Pages 29-44, https://doi.org/10.1016/j.jmva.2017.02.011
Keywords:	Multivariate Truncated Moments; Quadratic Forms; Elliptical Truncation; Tail Moments; Parametric Distributions; Elliptical Functions;
Academic Unit:	Faculty of Social Sciences > Economics, Finance and Accounting
Item ID:	9145
Depositing User:	Juan Arismendi Zambrano
Date Deposited:	15 Jan 2018 16:06
Publisher:	SSRN
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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