新架构让深度网络高效学习鞅过程，用于金融衍生品定价。
A new architecture of high-order deep neural networks that learn martingales
- 基于高阶弱逼近算法，仅通过向量场的迭代与线性组合实现
- 在金融衍生品定价任务中表现优于传统方法
- 适合研究金融计算与随机微分方程的模型设计者
提出一种基于随机微分方程（SDE）高阶弱逼近算法的新型深度神经网络架构。该架构利用显式龙格-库塔型高阶弱逼近方法，仅通过目标SDE向量场的迭代组合与线性组合实现近似，使深度神经网络能够高效学习鞅过程。研究还分析了该架构在金融衍生品定价问题上的表现。
原文摘要 · Abstract (English)
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.
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