A stein type lemma for the multivariate generalized hyperbolic distribution

Steven Vanduffel () and Jing Yao

European Journal of Operational Research, 2017, vol. 261, issue 2, 606-612

Abstract: 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.

Keywords: Decision analysis; Utility function; Stein’s lemma; Mean–variance optimization; Multivariate generalized hyperbolic distribution (MGH) (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:261:y:2017:i:2:p:606-612

DOI: 10.1016/j.ejor.2017.03.008

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