A Probabilistic Solution to High-Dimensional Continuous-Time Macro-Finance Models

This paper demonstrates that the equilibrium dynamics of a continuous-time macro-finance model can be characterized by the probabilistic solution of a coupled forward-backward stochastic differential equation. The probabilistic approach can, to some extent, overcome the ``curse of dimensionality'' with the help of the parametric approximation of deep neural networks and Machine Learning libraries (e.g., TensorFlow in Python and Flux in Julia). I propose a simple algorithm and assess its performance by considering a multiple-country macro-finance model, which allows for an analytic solution under symmetric states