Simulation of BSDEs by Wiener chaos expansion
type: Item
instance of: scholarly article
title: Simulation of BSDEs by Wiener chaos expansion
zbMATH Open document ID: 1311.60077
DOI: 10.1214/13-AAP943
author: Philippe Briand
author: Céline Labart
published in: The Annals of Applied Probability
publication date: 2014-06-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1204.4137
full work available at URL: https://projecteuclid.org/euclid.aoap/1398258097
review text: The authors consider the numerical approximation of solutions \((Y,Z)\) to real, scalar backward stochastic differential equations of the form \[ Y_t = \xi + \int_t^T f(s,Y_s,Z_s)ds -\int_t^T Z_s \cdot dB_s, \;\;0\leq t\leq T \] with real terminal random variable \(\xi\) and \(B\) being a \(d\)-dimensional Brownian motion. The paper presents a numerical scheme based on Wiener chaos expansion (of finite order) and Picard iteration. In particular, the scheme is a forward scheme calculating the necessary conditional expectations with chaos decomposition formulas; \(Z\) is computed via the Malliavin derivative. The convergence of the algorithm is established under suitable hypotheses, error bounds are computed and numerical experiments are carried out illustrating the theoretical results.
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60H07
zbMATH DE Number: 6304079
zbMATH Keywords: backward stochastic differential equations
zbMATH Keywords: numerical approximation
zbMATH Keywords: Wiener chaos expansion
zbMATH Keywords: Malliavin derivative
reviewed by: Martin Georg Riedler
MaRDI profile type: Publication
arXiv ID: 1204.4137
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description: scientific article