# Mathematics of Differential Machine Learning in Derivative Pricing and Hedging

arXiv: https://arxiv.org/abs/2405.01233 · HTML: https://mlsanity.com/paper/2405.01233/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 22 references that are in the map.
- First posted on arXiv 2 May 2024.

## Builds on (most cited first, 2 of 2)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Power of Depth for Feedforward Neural Networks](https://mlsanity.com/paper/1512.03965/) (2015)

## Built on by (most cited first, 2 of 2)

- [Dynamic Hedging Strategies in Derivatives Markets with LLM-Driven Sentiment and News Analytics](https://mlsanity.com/paper/2504.04295/) (2025)
- [Differential Machine Learning for Time Series Prediction](https://mlsanity.com/paper/2503.03302/) (2025)

## Abstract (arXiv)

This article introduces the groundbreaking concept of the financial differential machine learning algorithm through a rigorous mathematical framework. Diverging from existing literature on financial machine learning, the work highlights the profound implications of theoretical assumptions within financial models on the construction of machine learning algorithms. This endeavour is particularly timely as the finance landscape witnesses a surge in interest towards data-driven models for the valuation and hedging of derivative products. Notably, the predictive capabilities of neural networks have garnered substantial attention in both academic research and practical financial applications. The approach offers a unified theoretical foundation that facilitates comprehensive comparisons, both at a theoretical level and in experimental outcomes. Importantly, this theoretical grounding lends substantial weight to the experimental results, affirming the differential machine learning method's optimality within the prevailing context. By anchoring the insights in rigorous mathematics, the article bridges the gap between abstract financial concepts and practical algorithmic implementations.