Solving High-Dimensional Dynamic Programming Problems in Economics

A wide range of essential economic questions require solving high-dimensional dynamic programming problems. These problems suffer from the “curse of dimensionality”, which means that the computational complexity and memory requirements increase exponentially with the number of variables of the problem. The aim of this project is twofold" first, to develop a reliable deep-learning algorithm that can efficiently calculate a global solution to this class of problems; second, to compare this approach to another promising method based on functional tensor train decomposition of the involved value function and optimum policy function. We plan to elaborate and compare both these methodologies in a standard neoclassical growth model. Two specific applications will be studied: a multi-location model featuring multiple (50+) continuous state variables and a highly nonlinear migration model with 100+ continuous state variables.