We study the problem of ?finding the worst-case joint distribution of a set of risk factors given prescribed multivariate marginals and a nonlinear loss function. We show that when the risk measure is CVaR, and the distributions are discretized, the problem can be conveniently solved using...

An importance sampling approach for sampling copula models is introduced. We propose two algorithms that improve Monte Carlo estimators when the functional of interest depends mainly on the behaviour of the underlying random vector when at least one of the components is large. Such problems...

Motivated by too restrictive or even incorrect statements about generalized inverses in the literature, properties about these functions are investigated and proven. Examples and counterexamples show the importance of generalized inverses in mathematical theory and its applications. Copyright...

Motivated by too restrictive or even incorrect statements about generalized inverses in the literature, properties about these functions are investigated and proven. Examples and counterexamples show the importance of generalized inverses in mathematical theory and its applications. Copyright...

Companies in the same industry sector are usually more correlated than firms in different sectors, as they are similarly affected by macroeconomic effects, political decisions, and consumer trends. Despite the many stock return models taking this fact into account, there are only a few credit...

A probabilistic interpretation for hierarchical Archimedean copulas based on Lévy subordinators is given. Independent exponential random variables are divided by group-specific Lévy subordinators which are evaluated at a common random time. The resulting random vector has a hierarchical...

Nested Archimedean copulas recently gained interest since they generalize the well-known class of Archimedean copulas to allow for partial asymmetry. Sampling algorithms and strategies have been well investigated for nested Archimedean copulas. However, for likelihood based inference it is...