A new architecture of high-order deep neural networks that learn martingales

TL;DR

This paper introduces a novel deep neural network architecture inspired by high-order weak approximation algorithms for stochastic differential equations, enabling efficient learning of martingales, with applications in financial derivative pricing.

Contribution

It presents a new neural network design based on high-order weak approximation algorithms, advancing the ability to learn martingales in financial models.

Findings

Effective learning of martingales demonstrated

Application to financial derivatives pricing analyzed

Architecture based on Runge--Kutta type algorithms

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.