A generalized θ-scheme for solving backward stochastic differential equations

In this paper we propose a new type of θ-scheme with four parameters (\θᵢ\ᵢ₌₁⁴)for solving the backward stochastic differential equation -dyₜ=f(t,yₜ,zₜ) dt - zₜ dWₜ.We rigorously prove some error estimates for the proposed scheme, and in particular, we show that accuracy of the scheme can be high by choosing proper parameters. Various numerical examples are also presented to verify the theoretical results.