ODE-Based Multistep Schemes for Backward Stochastic Differential Equations  

作　　者：Shuixin Fang Weidong Zhao 

机构地区：[1]School of Mathematics&Institute of Finance,Shandong University,Jinan,Shandong 250100,P.R.China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2023年第4期1053-1086,共34页高等学校计算数学学报（英文版）

基　　金：supported by the National Natural Science Foundations of China(Grant Nos.12071261,11831010);the National Key R&D Program(Grant No.2018YFA0703900).

摘　　要：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.

关 键 词：Backward stochastic differential equation parabolic partial differential equation strong stability preserving linear multistep scheme high order discretization 

分 类 号：O17[理学—数学]