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.

翻译：本文提出了一类新型神经网络，其设计目标为输入变量的凸函数。该设计基于以下原理：任何凸函数均可表示为其所支配的仿射函数的上确界。这类神经网络对其输入具有固有的凸性，因此特别适用于逼近具有凸收益结构的期权价格。我们详细阐述了该网络的架构，并建立了理论收敛界以验证其逼近能力。同时，我们引入了一种“扰动”训练阶段以提升网络训练效果。最后，通过数值实验验证了该类网络在估计三类具有凸收益结构的期权（篮子期权、百慕大期权和摆动期权）价格方面的有效性。