We consider the problem where an agent aims to combine the views and insights of different experts' models. Specifically, each expert proposes a diffusion process over a finite time horizon. The agent then combines the experts' models by minimising the weighted Kullback-Leibler divergence to each of the experts' models. We show existence and uniqueness of the barycentre model and proof an explicit representation of the Radon-Nikodym derivative relative to the average drift model. We further allow the agent to include their own constraints, which results in an optimal model that can be seen as a distortion of the experts' barycentre model to incorporate the agent's constraints. Two deep learning algorithms are proposed to find the optimal drift of the combined model, allowing for efficient simulations. The first algorithm aims at learning the optimal drift by matching the change of measure, whereas the second algorithm leverages the notion of elicitability to directly estimate the value function. The paper concludes with a extended application to combine implied volatility smiles models that were estimated on different datasets.

翻译：我们考虑一个智能体旨在融合不同专家模型的观点与见解的问题。具体而言，每位专家提出一个有限时间范围内的扩散过程。随后，智能体通过最小化到各专家模型的加权Kullback-Leibler散度来融合这些专家模型。我们证明了重心模型的存在性与唯一性，并给出了相对于平均漂移模型的Radon-Nikodym导数的显式表示。我们进一步允许智能体加入自身的约束条件，这将产生一个最优模型，该模型可视为对专家重心模型的扭曲以纳入智能体的约束。本文提出了两种深度学习算法来求解组合模型的最优漂移，从而实现高效模拟。第一种算法旨在通过匹配测度变换来学习最优漂移，而第二种算法则利用可引出性概念直接估计价值函数。论文最后通过一个扩展应用，将基于不同数据集估计的隐含波动率微笑模型进行融合。