Stein's Lemma for elliptical random vectors

Zinoviy Landsman, Johanna Nešlehová

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)912-927
Number of pages16
JournalJournal of Multivariate Analysis
Volume99
Issue number5
DOIs
StatePublished - May 2008

Bibliographical 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.

Keywords

  • Density generator
  • Elliptical distribution
  • Generalized hyperbolic distribution
  • Normal distribution
  • Normal mixtures
  • Pearson Type VII distribution
  • Spherical distribution
  • Stein's Lemma
  • Student t distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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