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 …
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
We study a new algorithm for solving parabolic partial differential equations (PDEs) and
backward stochastic differential equations (BSDEs) in high dimension, which is based on an …
backward stochastic differential equations (BSDEs) in high dimension, which is based on an …
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning
In recent years, tremendous progress has been made on numerical algorithms for solving
partial differential equations (PDEs) in a very high dimension, using ideas from either …
partial differential equations (PDEs) in a very high dimension, using ideas from either …
[图书][B] A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black–Scholes partial differential equations
Artificial neural networks (ANNs) have very successfully been used in numerical simulations
for a series of computational problems ranging from image classification/image recognition …
for a series of computational problems ranging from image classification/image recognition …
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 backward schemes for high-dimensional nonlinear PDEs
We propose new machine learning schemes for solving high-dimensional nonlinear partial
differential equations (PDEs). Relying on the classical backward stochastic differential …
differential equations (PDEs). Relying on the classical backward stochastic differential …
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 …