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