Adapted $θ$-Scheme and Its Error Estimates for Backward Stochastic Differential Equations
This work offers an improved numerical method for solving BSDEs, which are important in finance and stochastic control, but the improvement appears incremental.
The authors propose a high-order numerical scheme for backward stochastic differential equations (BSDEs) by adaptively selecting the θ parameter per subinterval to reduce truncation errors, and provide error estimates verified by a numerical experiment.
In this paper we propose a new kind of high order numerical scheme for backward stochastic differential equations(BSDEs). Unlike the traditional $θ$-scheme, we reduce truncation errors by taking $θ$ carefully for every subinterval according to the characteristics of integrands. We give error estimates of this nonlinear scheme and verify the order of scheme through a typical numerical experiment.