A New Architecture of High-Order Deep Neural Networks that Learn Martingales

Yuming Ma () and Syoiti Ninomiya ()
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Yuming Ma: School of Engineering, Department of Engineering and Economics
Syoiti Ninomiya: School of Science, Department of Mathematics

A chapter in Stochastic Analysis and Applications 2025, 2026, pp 399-423 from Springer

Abstract: Abstract A new deep learning neural network architecture based on high-order weak approximation algorithms for stochastic differential equations (SDEs) is proposed. The architecture enables the efficient learning of martingales by deep learning models. The behaviour of deep neural networks based on this architecture, when applied to the problem of pricing financial derivatives, is also examined. The core of this new architecture lies in the high-order weak approximation algorithms of the explicit Runge–Kutta type, wherein the approximation is realised solely through iterative compositions and linear combinations of vector fields of the target SDEs.

Keywords: Primary 65C30; Secondary 60H35; 68T07; 91G60 (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-03914-9_14

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DOI: 10.1007/978-3-032-03914-9_14

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