Algorithm 368: Numerical inversion of Laplace transforms [D5]
Communications of the ACM
Comparison of sequence accelerators forthe Gaver method of numerical Laplace transform inversion
Computers & Mathematics with Applications
Efficiently sampling exchangeable Cuadras-Augé copulas in high dimensions
Information Sciences: an International Journal
Generating random numbers from a distribution specified by its Laplace transform
Statistics and Computing
Constructing hierarchical Archimedean copulas with Lévy subordinators
Journal of Multivariate Analysis
From Archimedean to Liouville copulas
Journal of Multivariate Analysis
Efficiently sampling nested Archimedean copulas
Computational Statistics & Data Analysis
Efficient maximum likelihood estimation of copula based meta t-distributions
Computational Statistics & Data Analysis
Journal of Multivariate Analysis
Numerical methods to quantify the model risk of basket default swaps
Journal of Computational and Applied Mathematics
Nonparametric estimation of the tree structure of a nested Archimedean copula
Computational Statistics & Data Analysis
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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 nested Archimedean copulas are presented. Moreover, for some Archimedean families, direct sampling algorithms are given. For other families, sampling algorithms based on numerical inversion of Laplace transforms are suggested. For this purpose, the Fixed Talbot, Gaver Stehfest, Gaver Wynn rho, and Laguerre series algorithm are compared in terms of precision and runtime. Examples are given, including both exchangeable and nested Archimedean copulas.