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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…

Numerical Analysis · Mathematics 2024-04-15 Lorenc Kapllani , Long Teng

We tackle high-dimensional, path-dependent valuation and control and introduce a deep BSDE/2BSDE solver that couples truncated log-signatures with a neural rough differential equation (RDE) backbone. The architecture aligns stochastic…

Mathematical Finance · Quantitative Finance 2025-11-04 Ali Atiah Alzahrani

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…

Numerical Analysis · Mathematics 2018-05-01 Kazufumi Ito , Yufei Zhang , Jun Zou

Using a combination of recurrent neural networks and signature methods from the rough paths theory we design efficient algorithms for solving parametric families of path dependent partial differential equations (PPDEs) that arise in pricing…

Computational Finance · Quantitative Finance 2020-11-24 Marc Sabate-Vidales , David Šiška , Lukasz Szpruch

Motivated by the idea of imposing paralleling computing on solving stochastic differential equations (SDEs), we introduce a new Domain Decomposition Scheme to solve forward-backward stochastic differential equations (FBSDEs) parallely. We…

Numerical Analysis · Mathematics 2010-08-03 Minh-Binh Tran

The problem of processing very long time-series data (e.g., a length of more than 10,000) is a long-standing research problem in machine learning. Recently, one breakthrough, called neural rough differential equations (NRDEs), has been…

Machine Learning · Computer Science 2022-04-20 Jaehoon Lee , Jinsung Jeon , Sheo yon Jhin , Jihyeon Hyeong , Jayoung Kim , Minju Jo , Kook Seungji , Noseong Park

We propose and study a scheme combining the finite element method and machine learning techniques for the numerical approximations of coupled nonlinear forward-backward stochastic partial differential equations (FBSPDEs) with homogeneous…

Numerical Analysis · Mathematics 2020-12-16 Hasib Uddin Molla , Jinniao Qiu

In this paper, we propose a deep learning based numerical scheme for strongly coupled FBSDEs, stemming from stochastic control. It is a modification of the deep BSDE method in which the initial value to the backward equation is not a free…

Optimization and Control · Mathematics 2023-02-10 Kristoffer Andersson , Adam Andersson , Cornelis W. Oosterlee

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…

Numerical Analysis · Mathematics 2024-08-13 Lorenc Kapllani , Long Teng

In this paper, we mainly focus on solving high-dimensional stochastic Hamiltonian systems with boundary condition, which is essentially a Forward Backward Stochastic Differential Equation (FBSDE in short), and propose a novel method from…

Optimization and Control · Mathematics 2021-12-13 Shaolin Ji , Shige Peng , Ying Peng , Xichuan Zhang

This work studies the deep learning-based numerical algorithms for optimal hedging problems in markets with general convex transaction costs on the trading rates, focusing on their scalability of trading time horizon. Based on the…

Mathematical Finance · Quantitative Finance 2022-12-29 Xiaofei Shi , Daran Xu , Zhanhao Zhang

In this paper, we introduce various machine learning solvers for (coupled) forward-backward systems of stochastic differential equations (FBSDEs) driven by a Brownian motion and a Poisson random measure. We provide a rigorous comparison of…

Numerical Analysis · Mathematics 2024-05-28 Clémence Alasseur , Zakaria Bensaid , Roxana Dumitrescu , Xavier Warin

The optimal stopping problem is one of the core problems in financial markets, with broad applications such as pricing American and Bermudan options. The deep BSDE method [Han, Jentzen and E, PNAS, 115(34):8505-8510, 2018] has shown great…

Probability · Mathematics 2023-08-28 Chengfan Gao , Siping Gao , Ruimeng Hu , Zimu Zhu

In this introductory paper, we discuss how quantitative finance problems under some common risk factor dynamics for some common instruments and approaches can be formulated as time-continuous or time-discrete forward-backward stochastic…

Computational Finance · Quantitative Finance 2019-11-29 Bernhard Hientzsch

In this paper, we propose a new first-order gradient-based algorithm to train deep neural networks. We first introduce the sign operation of stochastic gradients (as in sign-based methods, e.g., SIGN-SGD) into ADAM, which is called as…

Computer Vision and Pattern Recognition · Computer Science 2019-07-23 Dong Wang , Yicheng Liu , Wenwo Tang , Fanhua Shang , Hongying Liu , Qigong Sun , Licheng Jiao

We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, our algorithms estimate…

Probability · Mathematics 2020-06-08 Côme Huré , Huyên Pham , Xavier Warin

This paper presents a novel and direct approach to price boundary and final-value problems, corresponding to barrier options, using forward deep learning to solve forward-backward stochastic differential equations (FBSDEs). Barrier…

Computational Finance · Quantitative Finance 2024-09-13 Narayan Ganesan , Yajie Yu , Bernhard Hientzsch

This paper contributes to the challenge of learning a function on streamed multimodal data through evaluation. The core of the result of our paper is the combination of two quite different approaches to this problem. One comes from the…

Machine Learning · Computer Science 2019-09-24 Shujian Liao , Terry Lyons , Weixin Yang , Hao Ni

Deep neural networks (DNNs), especially physics-informed neural networks (PINNs), have recently become a new popular method for solving forward and inverse problems governed by partial differential equations (PDEs). However, these methods…

Machine Learning · Computer Science 2023-10-26 Wenbo Cao , Weiwei Zhang

In this paper, we propose a new methodology for state constrained stochastic optimal control (SOC) problems. The solution is based on past work in solving SOC problems using forward-backward stochastic differential equations (FBSDE). Our…

Systems and Control · Electrical Eng. & Systems 2021-04-07 Bolun Dai , Prashanth Krishnamurthy , Andrew Papanicolaou , Farshad Khorrami