We propose a Kronecker product structure for large covariance or correlation matrices. One feature of this model is that it scales logarithmically with dimension in the sense that the number of free parameters increases logarithmically with the dimension of the matrix. We propose an estimation...

In risk management, t-copulas are used to model dependencies beyond Gaussian copulas as they take into account tail dependencies. A t-copula has two parameters: the correlation matrix and the degree of freedom; they are usually estimated by maximizing the likelihood function of the observations....

Our contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we show that the intersection of the set of possible solutions and any orthant is convex.We derive a convex representation of this...

Increase of credit derivative transaction volumes and credit related exposures in trading books, contingent effect of the recent financial crisis along with insufficient measure of so called Value At Risk calculations raised new methodologies for credit risk models as well as input parameters...

This chapter presents the terminology and concepts of graph theory, and describes basic matrix operations that are used in social network analysis. Both graph theory and matrix operations have served as the foundations of many concepts in the analysis of social networks (Hage and Harary 1983;...

Mean-variance optimization provides a framework for constructing portfolios that have minimum risk for a given level of expected return. The required inputs are the expected asset returns, the asset covariance matrix, and a set of investment constraints. While portfolio optimization always leads...