🤖 AI Summary
This study addresses the challenge posed by the “curse of dimensionality,” which renders conventional numerical methods ineffective for high-dimensional dynamic stochastic models in economics and finance. To overcome this limitation, the work proposes an innovative integration of deep learning and dynamic economic modeling by combining deep equilibrium networks, physics-informed neural networks, differentiable surrogate models, and Gaussian processes. Enhanced with active learning and dimensionality reduction techniques, the proposed framework efficiently solves heterogeneous-agent, macro-financial, and climate-economy models characterized by extremely large continuous state spaces. The approach not only facilitates structural estimation and policy simulation but also substantially improves computational efficiency and estimation accuracy. Broad applicability is further supported through open-source, reproducible code.
📝 Abstract
This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality: heterogeneous-agent economies, overlapping-generations models with aggregate risk, continuous-time models with occasionally binding constraints, climate-economy models, and macro-finance environments with many assets and frictions generate state and parameter spaces that strain classical tensor-product grid methods. The exposition is organized around four complementary methodologies. Deep Equilibrium Nets embed discrete-time equilibrium conditions into neural-network loss functions. Physics-Informed Neural Networks approximate continuous-time Hamilton--Jacobi--Bellman, Kolmogorov forward, and related partial differential equations. Deep surrogate models provide fast, differentiable approximations to expensive structural models, while Gaussian processes add a probabilistic layer that quantifies approximation uncertainty; together they support estimation, sensitivity analysis, and constrained policy design. Gaussian-process-based dynamic programming, combined with active learning and dimension reduction, extends value-function iteration to very large continuous state spaces. Applications span representative-agent and international real business cycle models, overlapping-generations and heterogeneous-agent economies, continuous-time macro-finance, structural estimation by simulated method of moments, and climate economics under uncertainty. Companion notebooks in TensorFlow and PyTorch invite hands-on experimentation. These notes are a deliberately subjective and inevitably incomplete snapshot of a rapidly evolving field, aimed at equipping PhD students and researchers to engage with this frontier hands-on.