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...

Supplementary Appendix is available at: "https://ssrn.com/abstract=2970015" https://ssrn.com/abstract=2970015. Decision making in finance often requires an accurate estimate of the coskewness matrix to optimize the allocation to random variables with asymmetric distributions. The classical...

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...

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...

In this paper, we derive upper and lower bounds on the Range Value-at-Risk of the portfolio loss when we only know its mean and variance, and its feature of unimodality. In a first step, we use some classic results on stochastic ordering to reduce this optimization problem to a parametric one,...