Many financial decisions such as portfolio allocation, risk management, option pricing and hedge strategies are based on the forecast of the conditional variances, covariances and correlations of financial returns. Although the decisions are based on forecasts covariance matrix little is known...

We propose a novel approach to active risk management based on the recent Basel II regulations to obtain optimal portfolios with minimum capital requirements. In order to avoid regulatory penalties due to an excessive number of Value-at-Risk (VaR) violations, capital requirements are minimized...

This paper compares multivariate and univariate GARCH models to forecast portfolio value-at-risk (VaR). We provide a comprehensive look at the problem by considering realistic models and diversified portfolios containing a large number of assets, using both simulated and real data. Moreover, we...

Portfolio selection based on high dimensional covariance matrices is a key challenge in data-rich environments with the curse of dimensionality severely affecting most of the available covariance models. We challenge several multivariate Dynamic Conditional Correlation (DCC)-type and Stochastic...

In this paper, we focus on the estimation of a high-dimensional precision matrix. We propose a simple improvement of the graphical lasso framework (glasso) that is able to attain better statistical performance without sacrificing too much the computational cost. The proposed improvement is based...

In this paper we introduce a new multivariate stochastic order that compares random vectors in a direction which is determined by a unit vector, generalizing previous upper and lower orthant order. The main properties of this new order, together with its relationships with other multivariate...

We propose a new multivariate order based on a concept that we will call extremality". Given a unit vector, the extremality allows to measure the "farness" of a point with respect to a data cloud or to a distribution in the vector direction. We establish the most relevant properties of this...