A generalized $\theta$-scheme for solving backward stochastic differential equations
A generalized $\theta$-scheme for solving backward stochastic differential equations
In this paper we propose a new type of $\theta$-scheme with four parameters ($\{\theta_i\}_{i=1}^4$) for solving the backward stochastic differential equation $-dy_t=f(t,y_t,z_t) dt - z_t dW_t$. We rigorously prove some error estimates for the proposed scheme, and in particular, we show that accuracy of the scheme can be high by …