It has been frequently observed in the literature that many multivariate statistical methods require the covariance or dispersion matrix [Sigma] 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...

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...

We study copulas generated by elliptical distributions. We show that their tail dependence can be simply computed with default routines on Student's t-distribution given Kendall's [tau] and the tail index. The copula family generated by the sub-Gaussian [alpha]-stable distribution is unable to...

Many different robust estimation approaches for the covariance or shape matrix of multivariate data have been established. Tyler's M-estimator has been recognized as the 'most robust' M-estimator for the shape matrix of elliptically symmetric distributed data. Tyler's M-estimators for location...

A measure called 'extremal dependence coefficient' (EDC) is introduced for studying the asymptotic dependence structure of the minimum and the maximum of a random vector. Some general properties of the EDC are derived and its relation to the tail dependence coefficient is examined. The extremal...

In this paper, we derive two shrinkage estimators for minimum-variance portfolios that dominate the traditional estimator with respect to the out-of-sample variance of the portfolio return. The presented results hold for any number of assets d=4 and number of observations n=d+2. The small-sample...

In forecasting count processes, practitioners often ignore the discreteness of counts and compute forecasts based on Gaussian approximations instead. For both central and non-central point forecasts, and for various types of count processes, the performance of such approximate point forecasts is...

We develop a general approach to portfolio optimization taking account of estimation risk and stylized facts of empirical finance. This is done within a Bayesian framework. The approximation of the posterior distribution of the unknown model parameters is based on a parallel tempering algorithm....

We introduce a measure of diversification for portfolios comprising d risky assets. This measure relates the smallest possible return variance among these d assets to the overall portfolio return variance, yielding the portion of non-diversifiable risk. In the context of normally distributed...