Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations

Bruno Bouchard, Nizar Touzi

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)175-206
Number of pages32
JournalStochastic Processes and their Applications
Volume111
Issue number2
DOIs
StatePublished - Jun 2004

Keywords

  • Malliavin calculus
  • Monte-Carlo methods for (reflected) forward-backward SDEs
  • Regression estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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