Machine Learning for Continuous-Time Economics

Abstract

This paper proposes a global algorithm to solve a large class of nonlinear continuous-time models in finance and economics. Using tools from machine learning, I recast problem of solving the corresponding nonlinear partial differential equations as a sequence of supervised learning problems. To illustrate the scope of the method, I solve nontrivial benchmark models and compare the numerical solution with the analytical ones. Furthermore, I propose a setting to test and evaluate solution methods. In the context of a neoclassical growth model, given any value function, the productivity function is reverse engineered so that the Hamilton-Jacobi-Bellman equation corresponding to the optimization problem is identically zero. This provides a testing ground for solution methods and an objective way of comparing them. Results indicate that the method is accurate and can handle nonlinear models with as many as 10 dimensions. Finally, I provide an open source library that implements the proposed algorithm.