Infinite-Horizon Optimal Control of Jump-Diffusion Models for Pollution-Dependent Disasters

TL;DR

This paper develops a unified stochastic control framework for environmental risk in economic growth models, incorporating rare catastrophic shocks via jump-diffusion processes with pollution-dependent disaster risk.

Contribution

It introduces a general Poisson process-based formulation with closed-form solutions for non-local HJB equations, capturing pollution's role in amplifying macroeconomic vulnerability.

Findings

Disaster risk increases with pollution levels.

The model yields explicit solutions for optimal control policies.

Environmental degradation intensifies macroeconomic vulnerability.

Abstract

This paper is devoted to developing a unified framework for stochastic growth models with environmental risk, in which rare but catastrophic shocks interact with capital accumulation and pollution. The analysis is based upon a general Poisson point process formulation, leading to non-local Hamilton-Jacobi-Bellman (HJB) equations that admit closed-form candidate solutions and yield a composite state variable capturing exposure to rare shocks. We consider cases where disaster risk is endogenized through a pollution-dependent intensity and, in the more general cases, it also accommodates for state-dependent events of varying magnitude. Our formulation captures how environmental degradation amplifies macroeconomic vulnerability and strengthens incentives for abatement. From a technical perspective, it provides tractable jump-diffusion control problems whose HJB equation decomposes naturally into capital and pollution components under power-type value function.