Deep Kusuoka Approximation: High-Order Spatial Approximation for Solving High-Dimensional Kolmogorov Equations and Its Application to Finance

The paper introduces a new deep learning-based high-order spatial approximation for a solution of a high-dimensional Kolmogorov equation where the initial condition is only assumed to be a continuous function and the condition on the vector fields associated with the differential operator is very ge...

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Bibliographic Details
Published in:	Computational economics Vol. 64; no. 3; pp. 1443 - 1461
Main Authors:	Naito, Riu, Yamada, Toshihiro
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.09.2024 Springer Springer Nature B.V
Subjects:	Approximation Behavioral/Experimental Economics Computation Computational mathematics Computer Appl. in Social and Behavioral Sciences Deep learning Differential equations Differentiation Economic Theory/Quantitative Economics/Mathematical Methods Economics Economics and Finance Fields (mathematics) Learning Math Applications in Computer Science Mathematical analysis Neural networks Numerical differentiation Operations Research/Decision Theory Operators (mathematics) Optimization techniques Partial differential equations Random variables Viscosity Deep learning Financial diffusions Kolmogorov equations Kusuoka approximation Delta computing
ISSN:	0927-7099, 1572-9974
Online Access:	Get full text
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