Mean-field neural networks: Learning mappings on Wasserstein space.

We study the machine learning task for models with operators mapping between the Wasserstein space of probability measures and a space of functions, like e.g. in mean-field games/control problems.

The GroupMax Neural Network Approximation of Convex Functions.

We present a new neural network to approximate convex functions. This network has the particularity to approximate the function with cuts which is, for example, a necessary feature to approximate Bellman values when solving linear stochastic optimization problems. The network can be easily adapted to partial convexity.

Incentives, lockdown, and testing: from Thucydides' analysis to the COVID-19 pandemic.

In this work, we provide a general mathematical formalism to study the optimal control of an epidemic, such as the COVID-19 pandemic, via incentives to lockdown and testing. In particular, we model the interplay between the government and the population as a principal-agent problem with moral hazard, à la Cvitanić et al. (Finance Stoch 22(1):1-37, 2018), while an epidemic is spreading according to dynamics given by compartmental stochastic SIS or SIR models, as proposed respectively by Gray et al.