Applications of Deep Learning-Based Probabilistic Approach to Economic Models with High-Dimensional Controls

Abstract

In this paper, we combine a deep learning-based probabilistic approach with the finite volume method to numerically solve the equilibrium of economic models with infinite-dimensional controls. We consider two examples to demonstrate the implementation of our method. The first example involves the debt-maturity management problem in a stochastic, time-varying environment, where the infinite-dimensional outstanding debt profile serves as a controlled state variable. In the second example, we explore a preferred habitat model for the term structure of interest rates, where financial intermediaries allocate their portfolios among debt instruments with a continuum of different maturities

Keywords: JEL Classification: C63, F34, E43 backward stochastic differential equation, deep learning, finite volume method, debt maturity management, term structure of interest rates