It has been frequently observed in the literature that many multivariate statistical methods require the covariance or dispersion matrix S of an elliptical distribution only up to some scaling constant. If the topic of interest is not the scale but only the shape of the elliptical distribution,...

Suppose that we are searching for the maximum of many unknown and analytically untractable quantities or, say, the "best alternative" among several candidates. If our decision is based on historical or simulated data there is some sort of selection bias and it is not evident if our choice is...

"This book is refreshing, innovative and important for several reasons. Perhaps most importantly, it attempts to reconcile game theory with one-person decision theory by viewing a game as a collection of one-person decision problems. As natural as this approach may seem, it is hard to find game...

Traditional portfolio optimization has been often criticized since it does not account for estimation risk. Theoretical considerations indicate that estimation risk is mainly driven by the parameter uncertainty regarding the expected asset returns rather than their variances and covariances....

In recent publications standard methods of random matrix theory were applied to principal components analysis of high-dimensional financial data. We discuss the fundamental results and potential shortcomings of random matrix theory in the light of the stylized facts of empirical finance....

Two shrinkage estimators for the global minimum variance portfolio that dominate the traditional estimator with respect to the out-of-sample variance of the portfolio return are derived. The presented results hold for any number of observations n = d 2 and number of assets d = 4. The...