The purpose of this paper is to investigate the numerical solutions to two-dimensional forward backward stochastic differential equations(FBSDEs). Based on the Fourier cos-cos transform, the approximations of conditional expectations and their errors are studied with conditional characteristic functions. A new numerical scheme is proposed by using the least-squares regression-based Monte Carlo method to solve the initial value of FBSDEs. Finally, a numerical experiment in European option pricing is implemented to test the efficiency and stability of this scheme.

中文翻译：

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基于回归的蒙特卡洛方法求解二维正向后向随机微分方程

本文的目的是研究二维正向后向随机微分方程（FBSDE）的数值解。基于傅立叶cos-cos变换，利用条件特征函数研究条件期望的逼近及其误差。提出了一种基于最小二乘回归的蒙特卡罗方法求解FBSDEs的初值的新数值方案。最后，在欧洲期权定价中进行了数值实验，以测试该方案的效率和稳定性。