A framework for adaptive Monte Carlo procedures

DOI10.1515/MCMA.2011.002zbMath1223.65003arXiv1001.3551MaRDI QIDQ3168631

Jérôme Lelong, Bernard Lapeyre

Publication date: 19 April 2011

Published in: Monte Carlo Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.3551

zbMATH Keywords

convergenceimportance samplingstochastic approximationBrownian motionnumerical experimentsMonte Carlo methodsadaptive algorithmcentral limit theoremvariance reductionbasket optionsrisk neutral measurelocal volatility modelexpectation with free parameter

Mathematics Subject Classification ID

Related Items (11)

Coupling importance sampling and multilevel Monte Carlo using sample average approximation ⋮ Importance sampling and statistical Romberg method ⋮ Adaptive importance sampling for multilevel Monte Carlo Euler method ⋮ Batching Adaptive Variance Reduction ⋮ Robust adaptive numerical integration of irregular functions with applications to basket and other multi-dimensional exotic options ⋮ Adaptive importance sampling Monte Carlo simulation for general multivariate probability laws ⋮ Adaptive importance sampling and control variates ⋮ On sample average approximation algorithms for determining the optimal importance sampling parameters in pricing financial derivatives on Lévy processes ⋮ Convergence rates for optimised adaptive importance samplers ⋮ Convergence of Markovian Stochastic Approximation with Discontinuous Dynamics ⋮ Automatic control variates for option pricing using neural networks

Cites Work

• Adaptive Monte Carlo variance reduction for Lévy processes with two-time-scale stochastic approximation
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• Proofs of the martingale FCLT
• Robust adaptive importance sampling for normal random vectors
• Unconstrained recursive importance sampling
• Asymptotically Optimal Importance Sampling and Stratification for Pricing Path-Dependent Options
• Stochastic Approximation with Averaging of the Iterates: Optimal Asymptotic Rate of Convergence for General Processes
• Central limit theorems for local martingales
• Acceleration of Stochastic Approximation by Averaging
• Asymptotic Almost Sure Efficiency of Averaged Stochastic Algorithms
• Adaptative Monte Carlo Method, A Variance Reduction Technique
• Optimal Importance Sampling Parameter Search for Lévy Processes via Stochastic Approximation
• Adaptive Control Variates for Finite-Horizon Simulation
• A Stochastic Approximation Method

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