新神经网络可直接学习期权价格的凸函数关系，提升定价精度。
A new Input Convex Neural Network with application to options pricing
- 用仿射函数上确界构建输入凸神经网络
- 在篮子、美式与灵活交易期权上实现高精度定价
- 适合金融工程中需保证凸性的建模场景
我们提出一类新的神经网络，其输出对输入为凸函数，基于任意凸函数可表示为其支配的仿射函数上确界的原理。该网络天然具有输入凸性，特别适用于逼近具有凸收益结构的期权价格。文中详述了其架构，并建立了理论收敛边界以验证其近似能力。此外，引入了‘打乱’训练阶段以提升训练效果。数值实验表明，该网络在三类凸收益期权——篮子期权、美式期权和灵活交易期权——的定价中均表现有效。
原文摘要 · Abstract (English)
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 \emph{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.
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