An overview on deep learning-based approximation methods for partial differential equations
C Beck, M Hutzenthaler, A Jentzen… - arXiv preprint arXiv …, 2020 - arxiv.org
It is one of the most challenging problems in applied mathematics to approximatively solve
high-dimensional partial differential equations (PDEs). Recently, several deep learning …
high-dimensional partial differential equations (PDEs). Recently, several deep learning …
Recent developments in machine learning methods for stochastic control and games
R Hu, M Lauriere - arXiv preprint arXiv:2303.10257, 2023 - arxiv.org
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 …
economics to social sciences, robotics, and energy management. Many real-world …
[图书][B] Backward stochastic differential equations
J Zhang, J Zhang - 2017 - Springer
Backward Stochastic Differential Equations | SpringerLink Skip to main content Advertisement
SpringerLink Account Menu Find a journal Publish with us Track your research Search Cart …
SpringerLink Account Menu Find a journal Publish with us Track your research Search Cart …
New kinds of high-order multistep schemes for coupled forward backward stochastic differential equations
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 …
backward stochastic differential equations (FBSDEs). Based on the FBSDEs theory, we …
Numerical methods for backward stochastic differential equations: A survey
J Chessari, R Kawai, Y Shinozaki… - Probability Surveys, 2023 - projecteuclid.org
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 …
various areas of social and natural sciences, such as the pricing and hedging of financial …
Linear multistep schemes for BSDEs
JF Chassagneux - SIAM Journal on Numerical Analysis, 2014 - SIAM
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 …
stochastic differential equations (BSDEs). We show that, under a sufficient condition on the …
[PDF][PDF] 不确定性量化的高精度数值方法和理论
汤涛， 周涛 - 中国科学: 数学, 2015 - math.hkbu.edu.hk
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 …
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 multi-dimensional backward stochastic differential equations
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 …
equations (BSDEs) based on a multi-step time discretization scheme [31] is presented. In the …
Convergence of the backward deep BSDE method with applications to optimal stopping problems
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 [J …
applications such as pricing American and Bermudan options. The deep BSDE method [J …
EFFICIENT SPECTRAL SPARSE GRID APPROXIMATIONS FOR SOLVING MULTI-DIMENSIONAL FORWARD BACKWARD SDES.
This is the second part of a series papers on multi-step schemes for solving coupled forward
backward stochastic differential equations (FBSDEs). We extend the basic idea in our former …
backward stochastic differential equations (FBSDEs). We extend the basic idea in our former …