Necessary and sufficient conditions for the subadditivity of Value-at-Risk (V aRα) for portfolios of bonds are presented under various dependence assumptions. For sufficiently large α, V aRα is subadditive. However, for any α one can construct portfolios for which V aRα is superadditive.

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...

A new class of copulas referred to as “Sibuya copulas” is introduced and its properties are investigated. Members of this class are of a functional form which was first investigated in the work of M. Sibuya. The construction of Sibuya copulas is based on an increasing stochastic process...

The challenge of efficiently sampling exchangeable and nested Archimedean copulas is addressed. Specific focus is put on large dimensions, where methods involving generator derivatives are not applicable. Additionally, new conditions under which Archimedean copulas can be mixed to construct...

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...

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...

Efficient sampling algorithms for both Archimedean and nested Archimedean copulas are presented. First, efficient sampling algorithms for the nested Archimedean families of Ali-Mikhail-Haq, Frank, and Joe are introduced. Second, a general strategy how to build a nested Archimedean copula from a...