The AEP algorithm for the fast computation of the distribution of the sum of dependent random variables

DOI10.3150/10-BEJ284zbMath1248.60018arXiv1106.2920OpenAlexW2052874426MaRDI QIDQ453289

Paul Embrechts, Philipp Arbenz, Giovanni Puccetti

Publication date: 19 September 2012

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.2920

zbMATH Keywords

convolutiondistribution functions

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Probability distributions: general theory (60E05) Distribution theory (60E99)

Related Items (20)

Risk Measures and Multivariate Extensions of Breiman's Theorem ⋮ Copula-based measurement error models ⋮ A Conversation With Paul Embrechts ⋮ Computing the distribution of the sum of dependent random variables via overlapping hypercubes ⋮ When copulas and smoothing met: an interview with Irène Gijbels ⋮ A modified version of stochastic dominance involving dependence ⋮ High level quantile approximations of sums of risks ⋮ Unnamed Item ⋮ Simple risk measure calculations for sums of positive random variables ⋮ A note on the computation of sharp numerical bounds for the distribution of the sum, product or ratio of dependent risks ⋮ Archimedean copulas with applications to VaR estimation ⋮ Tail approximations for sums of dependent regularly varying random variables under Archimedean copula models ⋮ On the distribution of sums of random variables with copula-induced dependence ⋮ A comprehensive family of copulas to model bivariate random noise and perturbation ⋮ Risk aggregation with empirical margins: Latin hypercubes, empirical copulas, and convergence of sum distributions ⋮ Simulation methods for robust risk assessment and the distorted mix approach ⋮ Aggregation of log-linear risks ⋮ ASSET DEPENDENCY STRUCTURES AND PORTFOLIO INSURANCE STRATEGIES ⋮ The GAEP algorithm for the fast computation of the distribution of a function of dependent random variables ⋮ The Mean of Marshall–Olkin-Dependent Exponential Random Variables

Uses Software

• QRM

Cites Work

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• An introduction to copulas.
• Searching for extensible Korobov rules
• Some asymptotic results for sums of dependent random variables, with actuarial applications
• Stochastic simulation: Algorithms and analysis
• Variance Reduction via Lattice Rules
• Bounded Relative Error Importance Sampling and Rare Event Simulation
• On the Tail Behavior of Sums of Dependent Risks
• Generating Quasi-Random Paths for Stochastic Processes

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