Related papers: FBSJNN: A Theoretically Interpretable and Efficien…

Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…

In this article, we investigate the existence of a deep neural network (DNN) capable of approximating solutions to partial integro-differential equations while circumventing the curse of dimensionality. Using the Feynman-Kac theorem, we…

We propose the first learning scheme for functional differential equations (FDEs). FDEs play a fundamental role in physics, mathematics, and optimal control. However, the numerical analysis of FDEs has faced challenges due to its…

Recently proposed numerical algorithms for solving high-dimensional nonlinear partial differential equations (PDEs) based on neural networks have shown their remarkable performance. We review some of them and study their convergence…

In this work, we propose a novel backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs), where the deep neural network (DNN) models are trained not only…

We propose some numerical schemes for forward-backward stochastic differential equations (FBSDEs) based on a new fundamental concept of transposition solutions. These schemes exploit time-splitting methods for the variation of constants…

Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal grids. Inspired by modern deep learning based techniques for…

Recent advances in deep learning makes solving parabolic partial differential equations (PDEs) in high dimensional spaces possible via forward-backward stochastic differential equation (FBSDE) formulations. The implementation of most…

We study the error arising in the numerical approximation of FBSDEs and related PIDEs by means of a deep learning-based method. Our results focus on decoupled FBSDEs with jumps and extend the seminal work of HAn and Long (2020) analyzing…

We propose a new multistep deep learning-based algorithm for the resolution of moderate to high dimensional nonlinear backward stochastic differential equations (BSDEs) and their corresponding parabolic partial differential equations (PDE).…

In this work, we present a novel forward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs). Motivated by the fact that differential deep learning can…

In this paper, we study forward-backward doubly stochastic differential equations driven by Brownian motions and Poisson process (FBDSDEP in short). Both the probabilistic interpretation for the solutions to a class of quasilinear…

The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…

In this paper,we mainly focus on the numerical solution of high-dimensional stochastic optimal control problem driven by fully-coupled forward-backward stochastic differential equations (FBSDEs in short) through deep learning. We first…

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

Machine learning for partial differential equations (PDEs) is a hot topic. In this paper we introduce and analyse a Deep BSDE scheme for nonlinear integro-PDEs with unbounded nonlocal operators -problems arising in e.g. stochastic control…

In this work, we study the numerical approximation of a class of singular fully coupled forward backward stochastic differential equations. These equations have a degenerate forward component and non-smooth terminal condition. They are…

We propose several algorithms to solve McKean-Vlasov Forward Backward Stochastic Differential Equations. Our schemes rely on the approximating power of neural networks to estimate the solution or its gradient through minimization problems.…

Recently, the deep learning method has been used for solving forward-backward stochastic differential equations (FBSDEs) and parabolic partial differential equations (PDEs). It has good accuracy and performance for high-dimensional…

Solving high dimensional partial differential equations (PDEs) has historically posed a considerable challenge when utilizing conventional numerical methods, such as those involving domain meshes. Recent advancements in the field have seen…