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Discrete-Time Approximation and Monte-Carlo Simulation of Backward Stochastic Differential Equations

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Date
2004
Dewey
Probabilités et mathématiques appliquées
Sujet
Méthode de Monte-Carlo; Numerical Probability
Journal issue
Stochastic Processes and their Applications
Volume
111
Number
2
Publication date
06-2004
Article pages
175-206
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.spa.2004.01.001
URI
https://basepub.dauphine.fr/handle/123456789/1804
Collections
  • CEREMADE : Publications
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Author
Touzi, Nizar
Bouchard, Bruno
Type
Article accepté pour publication ou publié
Abstract (EN)
We suggest a discrete-time approximation for decoupled forward–backward stochastic differential equations. The Lp norm of the error is shown to be of the order of the time step. Given a simulation-based estimator of the conditional expectation operator, we then suggest a backward simulation scheme, and we study the induced Lp error. This estimate is more investigated in the context of the Malliavin approach for the approximation of conditional expectations. Extensions to the reflected case are also considered. Author Keywords: Monte-Carlo methods for (reflected) forward–backward SDEs; Malliavin calculus; Regression estimation

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