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 editors: Geiss, Christel; Labart, Céline; Luoto, Antti

Journal or series: Advances in Applied Probability

ISSN: 0001-8678

eISSN: 1475-6064

Publication year: 2020

Volume: 52

Issue number: 3

Pages range: 735-771

Publisher: Cambridge University Press (CUP)

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1017/apr.2020.17

Publication open access: Not 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

Abstract

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.

Keywords: stochastic processes; differential equations; approximation; convergence

Free keywords: backward stochastic differential equations; approximation scheme; finite difference equation; convergence rate; random walk approximation

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 2