Arnulf Jentzen

TL;DR: A deep learning-based approach that can handle general high-dimensional parabolic PDEs using backward stochastic differential equations and the gradient of the unknown solution is approximated by neural networks, very much in the spirit of deep reinforcement learning with the gradient acting as the policy function.

TL;DR: In this article, a new algorithm for solving parabolic partial differential equations and backward stochastic differential equations (BSDEs) in high dimension, which is based on an analogy between the BSDE and reinforcement learning with the gradient of the solution playing the role of the policy function, and the loss function given by the error between the prescribed terminal condition and the solution of BSDE.

TL;DR: In this article, an explicit and easily implementable numerical method for such an SDE was proposed, which converges strongly with the standard order one-half to the exact solution of the SDE.

TL;DR: In this article, it was shown that for a large class of SDEs with non-globally Lipschitz continuous drift and diffusion coefficients, Euler's approximation converges neither in the strong mean-square sense nor in the numerically weak sense to the exact solution at a finite time point.

TL;DR: A new algorithm for solving parabolic partial differential equation (PDEs) and backward stochastic differential equations (BSDEs) in high dimension is studied, based on an analogy between the BSDE and reinforcement learning with the gradient of the solution playing the role of the policy function, and the loss function given by the error between the prescribed terminal condition and the solution of theBSDE.