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

Touzi, Nizar; Bouchard, Bruno (2004), Discrete-Time Approximation and Monte-Carlo Simulation of Backward Stochastic Differential Equations, Stochastic Processes and their Applications, 111, 2, p. 175-206. http://dx.doi.org/10.1016/j.spa.2004.01.001

Type
Article accepté pour publication ou publié
Date
2004
Journal name
Stochastic Processes and their Applications
Volume
111
Number
2
Publisher
Elsevier
Pages
175-206
Publication identifier
Metadata
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Author(s)
Touzi, Nizar
Bouchard, Bruno
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
Subjects / Keywords
Méthode de Monte-Carlo; Numerical Probability