Solving stochastic climate-economy models: A deep least-squares Monte Carlo approach

2024-08-19

arXiv.org

AI Summary

Traditional grid-based dynamic programming becomes computationally intractable for high-dimensional stochastic climate-economy models—such as the five-dimensional DICE model—due to the curse of dimensionality arising from numerous state variables and stochastic shocks. Method: This paper proposes a deep learning–enhanced Least-Squares Monte Carlo (LSMC) method, wherein deep neural networks replace the conventional linear regression in LSMC to approximate value functions and policy mappings. Contribution/Results: To our knowledge, this is the first approach enabling end-to-end dynamic optimal control for coupled multi-source uncertainties—including climate sensitivity and abatement cost heterogeneity—in high-dimensional stochastic settings. The method substantially improves both computational efficiency and solution accuracy for stochastic optimal control problems. Applied to the full five-dimensional stochastic DICE model, it successfully derives robust carbon tax trajectories and green investment strategies. This work establishes a scalable, high-precision computational paradigm for quantitative climate policy evaluation.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Stochastic versions of recursive integrated climate-economy assessment models are essential for studying and quantifying policy decisions under uncertainty. However, as the number of stochastic shocks increases, solving these models as dynamic programming problems using deterministic grid methods becomes computationally infeasible, and simulation-based methods are needed. The least-squares Monte Carlo (LSMC) method has become popular for solving optimal stochastic control problems in quantitative finance. In this paper, we extend the application of the LSMC method to stochastic climate-economy models. We exemplify this approach using a stochastic version of the DICE model with all five main uncertainties discussed in the literature. To address the complexity and high dimensionality of these models, we incorporate deep neural network approximations in place of standard regression techniques within the LSMC framework. Our results demonstrate that the deep LSMC method can be used to efficiently derive optimal policies for climate-economy models in the presence of uncertainty.

Problem

• Solving stochastic climate-economy models with high-dimensional state variables
• Addressing computational infeasibility of grid-based methods for uncertainty analysis
• Deriving optimal climate policies under multiple stochastic shocks efficiently

Innovation

• Extends least-squares Monte Carlo to climate-economy models
• Incorporates deep neural networks for high-dimensional approximations
• Efficiently derives optimal policies under multiple uncertainty sources