A1 Journal article (refereed)
Mean square rate of convergence for random walk approximation of forward-backward SDEs (2020)

Geiss, C., Labart, C., & Luoto, A. (2020). Mean square rate of convergence for random walk approximation of forward-backward SDEs. Advances in Applied Probability, 52(3), 735-771. https://doi.org/10.1017/apr.2020.17

JYU authors or editors

Publication details

All authors or editorsGeiss, Christel; Labart, Céline; Luoto, Antti

Journal or seriesAdvances in Applied Probability



Publication year2020


Issue number3

Pages range735-771

PublisherCambridge University Press (CUP)

Publication countryUnited Kingdom

Publication languageEnglish


Publication open accessNot open

Publication channel open access

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/73815

Web address of parallel published publication (pre-print)https://arxiv.org/abs/1807.05889


Let (Y, Z) denote the solution to a forward-backward stochastic differential equation (FBSDE). If one constructs a random walk from the underlying Brownian motion B by Skorokhod embedding, one can show -convergence of the corresponding solutions to We estimate the rate of convergence based on smoothness properties, especially for a terminal condition function in . The proof relies on an approximative representation of and uses the concept of discretized Malliavin calculus. Moreover, we use growth and smoothness properties of the partial differential equation associated to the FBSDE, as well as of the finite difference equations associated to the approximating stochastic equations. We derive these properties by probabilistic methods.

Keywordsstochastic processesdifferential equationsapproximationconvergence

Free keywordsbackward stochastic differential equations; approximation scheme; finite difference equation; convergence rate; random walk approximation

Contributing organizations

Ministry reportingYes

Reporting Year2020

JUFO rating2

Last updated on 2024-03-04 at 20:45