Year: 2023
Author: Shuixin Fang, Weidong Zhao
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 4 : pp. 1053–1086
Abstract
In this paper, we explore a new approach to design and analyze numerical schemes for backward stochastic differential equations (BSDEs). By the nonlinear Feynman-Kac formula, we reformulate the BSDE into a pair of reference ordinary differential equations (ODEs), which can be directly discretized by many standard ODE solvers, yielding the corresponding numerical schemes for BSDEs. In particular, by applying strong stability preserving (SSP) time discretizations to the reference ODEs, we can propose new SSP multistep schemes for BSDEs. Theoretical analyses are rigorously performed to prove the consistency, stability and convergency of the proposed SSP multistep schemes. Numerical experiments are further carried out to verify our theoretical results and the capacity of the proposed SSP multistep schemes for solving complex associated problems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2023-0060
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 4 : pp. 1053–1086
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 34
Keywords: Backward stochastic differential equation parabolic partial differential equation strong stability preserving linear multistep scheme high order discretization.