A new architecture of high-order deep neural networks that learn martingales
This work addresses a domain-specific problem in computational finance for derivative pricing, but appears incremental as it builds on existing approximation methods.
The authors tackled the problem of efficiently learning martingales by proposing a new deep neural network architecture based on high-order weak approximation algorithms for stochastic differential equations, and demonstrated its application to pricing financial derivatives.
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.