Fully Discrete Schemes and Their Analyses for Forward-Backward Stochastic Differential Equations
It provides a novel numerical approach for solving FBSDEs, which are important in mathematical finance and stochastic control, with proven convergence for a broad class of problems.
The paper proposes new numerical schemes for forward-backward stochastic differential equations (FBSDEs) using transposition solutions and time-splitting methods, proving convergence for various driver types and demonstrating effectiveness on nonlinear financial derivative pricing problems.
We propose some numerical schemes for forward-backward stochastic differential equations (FBSDEs) based on a new fundamental concept of transposition solutions. These schemes exploit time-splitting methods for the variation of constants formula of the associated partial differential equations and a discrete representation of the transition semigroups. The convergence of the schemes is established for FBSDEs with uniformly Lipschitz drivers, locally Lipschitz and maximal monotone drivers. Numerical experiments are presented for several nonlinear financial derivative pricing problems to demonstrate the adaptivity and effectiveness of the new schemes. The ideas here can be applied to construct high-order schemes for FBSDEs with general Markov forward processes.