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

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.