Solving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemes
DOI10.1007/s10915-022-02044-xzbMath1506.65174arXiv2012.07747OpenAlexW3113177434MaRDI QIDQ2680327
Nicolas Macris, Raffaele Marino
Publication date: 28 December 2022
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.07747
Kolmogorov equationnumerical analysisEuler-Maruyama approximationdeep learningLeimkuhler-Matthews approximationMilstein discretization
Numerical methods (including Monte Carlo methods) (91G60) Artificial neural networks and deep learning (68T07) Nonlinear parabolic equations (35K55) Derivative securities (option pricing, hedging, etc.) (91G20) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Rationality and learning in game theory (91A26) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)
Uses Software
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