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

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 state variables and stochastic shocks increases, solving these models via deterministic grid-based dynamic programming (e.g., value-function iteration / projection on a discretized grid over continuous state variables, typically coupled with discretized shocks) 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 five key uncertainty sources highlighted 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.