Mathematical modelling is ubiquitous in the financial industry and drives key
decision processes. Any given model provides only a crude approximation to
reality and the risk of using an inadequate model is hard to detect and
quantify. By contrast, modern data science techniques are opening the door to
more robust and data-driven model selection mechanisms. However, most machine
learning models are "black-boxes" as individual parameters do not have
meaningful interpretation. The aim of this paper is to combine the above
approaches achieving the best of both worlds. Combining neural networks with
risk models based on classical stochastic differential equations (SDEs), we
find robust bounds for prices of derivatives and the corresponding hedging
strategies while incorporating relevant market data. The resulting model called
neural SDE is an instantiation of generative models and is closely linked with
the theory of causal optimal transport. Neural SDEs allow consistent
calibration under both the risk-neutral and the real-world measures. Thus the
model can be used to simulate market scenarios needed for assessing risk
profiles and hedging strategies. We develop and analyse novel algorithms needed
for efficient use of neural SDEs. We validate our approach with numerical
experiments using both local and stochastic volatility models.

本文提出了一种结合神经网络和基于随机微分方程的经典风险模型的模型 —— 神经 SDE 模型，该模型可以根据市场数据进行一致性校准，并用于模拟市场场景以评估风险和对冲策略。

基于神经随机微分方程的稳健定价和对冲

Robust pricing and hedging via neural SDEs

Increasingly sophisticated mathematical modelling processes from Machine
Learning are being used to analyse complex data. However, the performance and
explainability of these models within practical critical systems requires a
rigorous and continuous verification of their safe utilisation. Working towards
addressing this challenge, this paper presents a principled novel safety
argument framework for critical systems that utilise deep neural networks. The
approach allows various forms of predictions, e.g., future reliability of
passing some demands, or confidence on a required reliability level. It is
supported by a Bayesian analysis using operational data and the recent
verification and validation techniques for deep learning. The prediction is
conservative -- it starts with partial prior knowledge obtained from lifecycle
activities and then determines the worst-case prediction. Open challenges are
also identified.

本文提出了一个基于贝叶斯分析的安全性论据框架，该框架使用运行数据和最新的深度学习验证技术，支持多种形式的预测，并针对实际的关键系统进行了建模和验证。