Stein's Lemma for elliptical random vectors

Zinoviy Landsman; Johanna Nešlehová

doi:10.1016/j.jmva.2007.05.006

Stein's Lemma for elliptical random vectors

Zinoviy Landsman, Johanna Nešlehová^*

^*Korrespondierende*r Autor*in für diese Arbeit

Publikation: Wissenschaftliche Fachzeitschrift › Originalbeitrag in Fachzeitschrift › Begutachtung

Abstract

For the family of multivariate normal distribution functions, Stein's Lemma presents a useful tool for calculating covariances between functions of the component random variables. Motivated by applications to corporate finance, we prove a generalization of Stein's Lemma to the family of elliptical distributions.

Originalsprache	Englisch
Seiten (von - bis)	912-927
Seitenumfang	16
Fachzeitschrift	Journal of Multivariate Analysis
Jahrgang	99
Ausgabenummer	5
DOIs	https://doi.org/10.1016/j.jmva.2007.05.006
Publikationsstatus	Veröffentlicht - Mai 2008
Extern publiziert	Ja

Bibliographische Notiz

Funding Information:
The first author acknowledges financial support by the FIM, ETH Zurich. The second author was supported by RiskLab, ETH Zurich. The authors thank Paul Embrechts for bringing Froot [8] to their attention and for fruitful discussions. They are grateful to the referees for their thorough comments and suggestions.

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10.1016/j.jmva.2007.05.006

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Zitat

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title = "Stein's Lemma for elliptical random vectors",

abstract = "For the family of multivariate normal distribution functions, Stein's Lemma presents a useful tool for calculating covariances between functions of the component random variables. Motivated by applications to corporate finance, we prove a generalization of Stein's Lemma to the family of elliptical distributions.",

keywords = "Density generator, Elliptical distribution, Generalized hyperbolic distribution, Normal distribution, Normal mixtures, Pearson Type VII distribution, Spherical distribution, Stein's Lemma, Student t distribution",

author = "Zinoviy Landsman and Johanna Ne{\v s}lehov{\'a}",

note = "Funding Information: The first author acknowledges financial support by the FIM, ETH Zurich. The second author was supported by RiskLab, ETH Zurich. The authors thank Paul Embrechts for bringing Froot [8] to their attention and for fruitful discussions. They are grateful to the referees for their thorough comments and suggestions.",

year = "2008",

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doi = "10.1016/j.jmva.2007.05.006",

language = "English",

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AU - Landsman, Zinoviy

AU - Nešlehová, Johanna

N1 - Funding Information: The first author acknowledges financial support by the FIM, ETH Zurich. The second author was supported by RiskLab, ETH Zurich. The authors thank Paul Embrechts for bringing Froot [8] to their attention and for fruitful discussions. They are grateful to the referees for their thorough comments and suggestions.

PY - 2008/5

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N2 - For the family of multivariate normal distribution functions, Stein's Lemma presents a useful tool for calculating covariances between functions of the component random variables. Motivated by applications to corporate finance, we prove a generalization of Stein's Lemma to the family of elliptical distributions.

AB - For the family of multivariate normal distribution functions, Stein's Lemma presents a useful tool for calculating covariances between functions of the component random variables. Motivated by applications to corporate finance, we prove a generalization of Stein's Lemma to the family of elliptical distributions.

KW - Density generator

KW - Elliptical distribution

KW - Generalized hyperbolic distribution

KW - Normal distribution

KW - Normal mixtures

KW - Pearson Type VII distribution

KW - Spherical distribution

KW - Stein's Lemma

KW - Student t distribution

U2 - 10.1016/j.jmva.2007.05.006

DO - 10.1016/j.jmva.2007.05.006

M3 - Journal article

AN - SCOPUS:40749116351

SN - 0047-259X

VL - 99

SP - 912

EP - 927

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 5

ER -