# A new Input Convex Neural Network with application to options pricing

arXiv: https://arxiv.org/abs/2411.12854 · HTML: https://mlsanity.com/paper/2411.12854/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 36 references that are in the map.
- First posted on arXiv 19 Nov 2024.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [How to Escape Saddle Points Efficiently](https://mlsanity.com/paper/1703.00887/) (2017)
- [Deep Learning without Poor Local Minima](https://mlsanity.com/paper/1605.07110/) (2016)
- [A Convergence Analysis of Gradient Descent for Deep Linear Neural Networks](https://mlsanity.com/paper/1810.02281/) (2018)
- [Learning One-hidden-layer Neural Networks with Landscape Design](https://mlsanity.com/paper/1711.00501/) (2017)
- [Learning deep linear neural networks: Riemannian gradient flows and convergence to global minimizers](https://mlsanity.com/paper/1910.05505/) (2019)
- [Width Provably Matters in Optimization for Deep Linear Neural Networks](https://mlsanity.com/paper/1901.08572/) (2019)
- [The loss landscape of deep linear neural networks: a second-order analysis](https://mlsanity.com/paper/2107.13289/) (2021)
- [The GroupMax neural network approximation of convex functions](https://mlsanity.com/paper/2206.06622/) (2022)
- [Deep multitask neural networks for solving some stochastic optimal control problems](https://mlsanity.com/paper/2401.12923/) (2024)

## Abstract (arXiv)

We introduce a new class of neural networks designed to be convex functions of their inputs, leveraging the principle that any convex function can be represented as the supremum of the affine functions it dominates. These neural networks, inherently convex with respect to their inputs, are particularly well-suited for approximating the prices of options with convex payoffs. We detail the architecture of this, and establish theoretical convergence bounds that validate its approximation capabilities. We also introduce a scrambling phase to improve the training of these networks. Finally, we demonstrate numerically the effectiveness of these networks in estimating prices for three types of options with convex payoffs: Basket, Bermudan, and Swing options.