  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.
