A stein type lemma for the multivariate generalized hyperbolic distribution

Steven Vanduffel, Jing Yao*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


When two variables are bivariate normally distributed, Stein's (1973, 1981) seminal lemma provides a convenient expression for the covariance of the first variable with a function of the second. The lemma has proven to be useful in various disciplines, including statistics, probability, decision theory and finance. In finance, however, asset returns do not always display symmetry but may exhibit skewness. This observation led Adcock (2007, 2010, 2014) to develop Stein's type lemmas for certain multivariate distributions that are consistent with Simaan's (1987, 1993) setting for asset returns. In this paper, we depart from Simaan's setting and develop a new Stein's type lemma in the setting of a mean–variance mixture model for returns. As a particular application, we show that expected utility maximizers select portfolios that are mean–variance–skewness efficient.

Original languageEnglish
Pages (from-to)606-612
Number of pages7
JournalEuropean Journal of Operational Research
Issue number2
Early online date14 Mar 2017
Publication statusPublished - 1 Sept 2017


  • Decision analysis
  • Mean–variance optimization
  • Multivariate generalized hyperbolic distribution (MGH)
  • Stein's lemma
  • Utility function

ASJC Scopus subject areas

  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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