Deep Operator BSDE: a Numerical Scheme to Approximate the Solution Operators
Motivated by dynamic risk measures and conditional $g$-expectations, in this work we propose a numerical method to approximate the solution operator given by a Backward Stochastic Differential Equation (BSDE). The main ingredients for this are the Wiener chaos decomposition and the classical Euler scheme for BSDEs. We show convergence of this scheme under very mild assumptions, and provide a rate of convergence in more restrictive cases. We then implement it using neural networks, and we present several numerical examples where we can check the accuracy of the method.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations
Deep learning-based numerical schemes for solving high-dimensional backward stochastic differential equations (BSDEs) have recently raised plenty of scientific interest. While they enable numerical methods to approximate…
Deep LearningUncertainty QuantificationSimultaneously Solving FBSDEs and their Associated Semilinear Elliptic PDEs with Small Neural Operators
Forward-backwards stochastic differential equations (FBSDEs) play an important role in optimal control, game theory, economics, mathematical finance, and in reinforcement learning. Unfortunately, the available FBSDE solv…
Mean-variance portfolio selection under partial information with drift uncertainty
In this paper, we study the mean-variance portfolio selection problem under partial information with drift uncertainty. First we show that the market model is complete even in this case while the information is not compl…
A Fourier interpolation method for numerical solution of FBSDEs: Global convergence, stability, and higher order discretizations
The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs), introduced in [21], uses a uniform space grid. In this paper we utilize a tree-like spatial discretization…
Spatial InterpolationDiscretization and Machine Learning Approximation of BSDEs with a Constraint on the Gains-Process
We study the approximation of backward stochastic differential equations (BSDEs for short) with a constraint on the gains process. We first discretize the constraint by applying a so-called facelift operator at times of …
BIG-bench Machine Learning