Many financial portfolios are optimized without taking the higher moments into account. We recommend tilting these portfolios in a direction that increases their estimated mean and third central moment and decreases their variance and fourth central moment. The advantages of tilting come at the...

Brown et al. (2006) derive a Stein-type inequality for the multivariate Student-t distribution. We generalize their result to the family of (multivariate) generalized hyperbolic distributions and derive a lower bound for the variance of a function of a random variable

When two random variables are bivariate normally distributed Stein's original lemma allows to conveniently express the covariance of the first variable with a function of the second. Landsman & Neslehova (2007) extend this seminal result to the family of multivariate elliptical distributions. In...