Open Access
Translator Disclaimer
October 2006 Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations
Jean-Philippe Lemor, Emmanuel Gobet, Xavier Warin
Author Affiliations +
Bernoulli 12(5): 889-916 (October 2006). DOI: 10.3150/bj/1161614951

Abstract

This study focuses on the numerical resolution of backward stochastic differential equations with data dependent on a jump-diffusion process. We propose and analyse a numerical scheme based on iterative regression functions which are approximated by projections on vector spaces of functions, with coefficients evaluated using Monte Carlo simulations. Regarding the error, we derive explicit bounds with respect to the time step, the number of paths simulated and the number of functions: this allows us to optimally adjust the parameters to achieve a given accuracy. We also present numerical tests related to option pricing with differential interest rates and locally risk-minimizing strategies (Föllmer-Schweizer decomposition).

Citation

Download Citation

Jean-Philippe Lemor. Emmanuel Gobet. Xavier Warin. "Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations." Bernoulli 12 (5) 889 - 916, October 2006. https://doi.org/10.3150/bj/1161614951

Information

Published: October 2006
First available in Project Euclid: 23 October 2006

zbMATH: 1136.60351
MathSciNet: MR2265667
Digital Object Identifier: 10.3150/bj/1161614951

Keywords: Backward stochastic differential equations , empirical regressions

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability

JOURNAL ARTICLE
28 PAGES


SHARE
Vol.12 • No. 5 • October 2006
Back to Top