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 …
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential …
High-dimensional partial differential equations (PDEs) appear in a number of models from
the financial industry, such as in derivative pricing models, credit valuation adjustment …
the financial industry, such as in derivative pricing models, credit valuation adjustment …
Deep splitting method for parabolic PDEs
C Beck, S Becker, P Cheridito, A Jentzen… - SIAM Journal on Scientific …, 2021 - SIAM
In this paper, we introduce a numerical method for nonlinear parabolic partial differential
equations (PDEs) that combines operator splitting with deep learning. It divides the PDE …
equations (PDEs) that combines operator splitting with deep learning. It divides the PDE …
[图书][B] Numerical solution of stochastic differential equations with jumps in finance
E Platen, N Bruti-Liberati - 2010 - books.google.com
In financial and actuarial modeling and other areas of application, stochastic differential
equations with jumps have been employed to describe the dynamics of various state …
equations with jumps have been employed to describe the dynamics of various state …
[图书][B] Stochastic modelling and applied probability
A Board - 2005 - Springer
During the seven years that elapsed between the first and second editions of the present
book, considerable progress was achieved in the area of financial modelling and pricing of …
book, considerable progress was achieved in the area of financial modelling and pricing of …
[图书][B] Stochastic numerics for mathematical physics
GN Milstein, MV Tretyakov - 2004 - Springer
This book is a substantially revised and expanded edition reflecting major developments in
stochastic numerics since the 1st edition [314] was published in 2004. The new topics …
stochastic numerics since the 1st edition [314] was published in 2004. The new topics …
[HTML][HTML] Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations
B Bouchard, N Touzi - Stochastic Processes and their applications, 2004 - Elsevier
We suggest a discrete-time approximation for decoupled forward–backward stochastic
differential equations. The Lp norm of the error is shown to be of the order of the time step …
differential equations. The Lp norm of the error is shown to be of the order of the time step …
A regression-based Monte Carlo method to solve backward stochastic differential equations
We are concerned with the numerical resolution of backward stochastic differential
equations. We propose a new numerical scheme based on iterative regressions on function …
equations. We propose a new numerical scheme based on iterative regressions on function …
A numerical scheme for BSDEs
J Zhang - The annals of applied probability, 2004 - projecteuclid.org
In this paper we propose a numerical scheme for a class of backward stochastic differential
equations (BSDEs) with possible path-dependent terminal values. We prove that our …
equations (BSDEs) with possible path-dependent terminal values. We prove that our …