Stochastic optimal control and games have a wide range of applications, from finance and
economics to social sciences, robotics, and energy management. Many real-world …

We give a survey of the developments in the theory of Backward Stochastic Differential
Equations during the last 20 years, including the solutions' existence and uniqueness …

In this work, we are concerned with the high-order numerical methods for coupled forward-
backward stochastic differential equations (FBSDEs). Based on the FBSDEs theory, we …

In this paper we propose a stable multistep scheme on time-space grids for solving
backward stochastic differential equations. In our scheme, the integrands, which are …

Abstract Backward Stochastic Differential Equations (BSDEs) have been widely employed in
various areas of social and natural sciences, such as the pricing and hedging of financial …

The aim of this paper is to carry out convergence analysis and algorithm implementation of a
novel sample-wise backpropagation method for training a class of stochastic neural …

We study the convergence rate of a class of linear multistep methods for backward
stochastic differential equations (BSDEs). We show that, under a sufficient condition on the …

In this work, we study solving (decoupled) forward-backward stochastic differential
equations (FBSDEs) numerically using the regression trees. Based on the general theta …

摘要不确定性量化(Uncertainty Quantification, UQ) 是近年来国际上热门的研究课题,
其应用领域包括水文学, 流体力学, 数据同化, 天气预测等等. 由于UQ 问题中的大量随机参数 …

A sparse-grid method for solving multi-dimensional backward stochastic differential
equations (BSDEs) based on a multi-step time discretization scheme [31] is presented. In the …