Asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors

Stefan Jaschke; Claudia Klüppelberg; Alexander Lindner

doi:10.1016/S0047-259X(03)00100-3

Asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors

Stefan Jaschke
, Claudia Klüppelberg
, Alexander Lindner

Chair of Mathematical Statistics

Fed. Financial Supervisor Authority
Technical University of Munich

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta-gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension.

Original language	English
Pages (from-to)	252-273
Number of pages	22
Journal	Journal of Multivariate Analysis
Volume	88
Issue number	2
DOIs	https://doi.org/10.1016/S0047-259X(03)00100-3
State	Published - Feb 2004

Keywords

Delta-gamma method
Quadratic forms of Gaussian vectors
Quantile estimation
Tail behavior
Value-at-Risk

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10.1016/S0047-259X(03)00100-3

Cite this

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title = "Asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors",

abstract = "We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta-gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension.",

keywords = "Delta-gamma method, Quadratic forms of Gaussian vectors, Quantile estimation, Tail behavior, Value-at-Risk",

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AU - Jaschke, Stefan

AU - Klüppelberg, Claudia

AU - Lindner, Alexander

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N2 - We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta-gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension.

AB - We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta-gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension.

KW - Delta-gamma method

KW - Quadratic forms of Gaussian vectors

KW - Quantile estimation

KW - Tail behavior

KW - Value-at-Risk

UR - https://www.scopus.com/pages/publications/0348222417

U2 - 10.1016/S0047-259X(03)00100-3

DO - 10.1016/S0047-259X(03)00100-3

M3 - Article

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SP - 252

EP - 273

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 2

ER -

Asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors

Abstract

Keywords

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