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 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 …
[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 …
Nonlinear expectations, nonlinear evaluations and risk measures
K Back, TR Bielecki, C Hipp, S Peng… - Stochastic Methods in …, 2004 - Springer
Introduction 1.1. Searching the Mechanism of Evaluations of Risky Assets 1.2. Axiomatic
Assumptions for Evaluations of Derivatives 1.3. Organization of the Lecture 2. Brownian …
Assumptions for Evaluations of Derivatives 1.3. Organization of the Lecture 2. Brownian …
Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs
For ad‐dimensional diffusion of the form dXt= μ (Xt) dt+ σ (Xt) dWt and continuous functions f
and g, we study the existence and uniqueness of adapted processes Y, Z, Γ, and A solving …
and g, we study the existence and uniqueness of adapted processes Y, Z, Γ, and A solving …
Solving high-dimensional optimal stopping problems using deep learning
S Becker, P Cheridito, A Jentzen… - European Journal of …, 2021 - cambridge.org
Nowadays many financial derivatives, such as American or Bermudan options, are of early
exercise type. Often the pricing of early exercise options gives rise to high-dimensional …
exercise type. Often the pricing of early exercise options gives rise to high-dimensional …
A quantization algorithm for solving multidimensional discrete-time optimal stopping problems
V Bally, G Pagès - Bernoulli, 2003 - projecteuclid.org
A new grid method for computing the Snell envelope of a function of an $\mathbb {R}^ d $-
valued simulatable Markov chain $(X_k) _ {0\lambda\leq k\lambda\leq n} $ is proposed.(This …
valued simulatable Markov chain $(X_k) _ {0\lambda\leq k\lambda\leq n} $ is proposed.(This …
Numerical probability
G Pagès - Universitext, Springer, 2018 - Springer
This book is an extended written version of the Master 2 course “Probabilités
Numériques”(ie, Numerical Probability or Numerical Methods in Probability) which has been …
Numériques”(ie, Numerical Probability or Numerical Methods in Probability) which has been …