A Machine Learning Algorithm for Finite-Horizon Stochastic Control Problems in Economics

TL;DR

This paper introduces a novel deep learning algorithm capable of efficiently solving high-dimensional, finite-horizon stochastic control problems in economics without relying on the Bellman equation, demonstrating superior convergence and applicability.

Contribution

The paper presents a new neural network-based method that handles high-dimensional, time-inhomogeneous stochastic control problems with guaranteed performance improvement and broad applicability.

Findings

Successfully solves problems with over 100 dimensions.

Demonstrates convergence through monotonic performance improvement.

Applies to complex models like stochastic volatility and climate-economy integration.

Abstract

We propose a machine learning algorithm for solving finite-horizon stochastic control problems based on a deep neural network representation of the optimal policy functions. The algorithm has three features: (1) It can solve high-dimensional (e.g., over 100 dimensions) and finite-horizon time-inhomogeneous stochastic control problems. (2) It has a monotonicity of performance improvement in each iteration, leading to good convergence properties. (3) It does not rely on the Bellman equation. To demonstrate the efficiency of the algorithm, it is applied to solve various finite-horizon time-inhomogeneous problems including recursive utility optimization under a stochastic volatility model, a multi-sector stochastic growth, and optimal control under a dynamic stochastic integration of climate and economy model with eight-dimensional state vectors and 600 time periods.