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 …
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 …
Machine learning for semi linear PDEs
Recent machine learning algorithms dedicated to solving semi-linear PDEs are improved by
using different neural network architectures and different parameterizations. These …
using different neural network architectures and different parameterizations. These …
[图书][B] Backward stochastic differential equations
J Zhang, J Zhang - 2017 - Springer
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Neural networks-based algorithms for stochastic control and PDEs in finance
This chapter presents machine learning techniques and deep reinforcement learning-based
algorithms for the efficient resolution of nonlinear partial differential equations and dynamic …
algorithms for the efficient resolution of nonlinear partial differential equations and dynamic …
Neural networks-based backward scheme for fully nonlinear PDEs
We propose a numerical method for solving high dimensional fully nonlinear partial
differential equations (PDEs). Our algorithm estimates simultaneously by backward time …
differential equations (PDEs). Our algorithm estimates simultaneously by backward time …
Optimal transportation under controlled stochastic dynamics
We consider an extension of the Monge-Kantorovitch optimal transportation problem. The
mass is transported along a continuous semimartingale, and the cost of transportation …
mass is transported along a continuous semimartingale, and the cost of transportation …
Branching diffusion representation of semilinear PDEs and Monte Carlo approximation
We provide a representation result of parabolic semi-linear PDEs, with polynomial
nonlinearity, by branching diffusion processes. We extend the classical representation for …
nonlinearity, by branching diffusion processes. We extend the classical representation for …
On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward …
Parabolic partial differential equations (PDEs) and backward stochastic differential
equations (BSDEs) are key ingredients in a number of models in physics and financial …
equations (BSDEs) are key ingredients in a number of models in physics and financial …
Approximation error analysis of some deep backward schemes for nonlinear PDEs
Recently proposed numerical algorithms for solving high-dimensional nonlinear partial
differential equations (PDEs) based on neural networks have shown their remarkable …
differential equations (PDEs) based on neural networks have shown their remarkable …