Infinite-Horizon Optimal Control of Jump-Diffusion Models for Pollution-Dependent Disasters
The paper develops a unified framework for stochastic growth models with environmental risk, in which rare but catastrophic shocks interact with capital accumul...
Abstract
The paper develops a unified framework for stochastic growth models with environmental risk, in which rare but catastrophic shocks interact with capital accumulation and pollution. The analysis begins with a Poisson process formulation, leading to a Hamilton-Jacobi-Bellman (HJB) equation with jump terms that admits closed-form candidate solutions and yields a composite state variable capturing exposure to rare shocks. The framework is then extended by endogenizing disaster intensity via a nonhomogeneous Poisson process, showing how environmental degradation amplifies macroeconomic risk and strengthens incentives for abatement. A further extension introduces pollution diffusion alongside state-dependent jump intensity, yielding a tractable jump-diffusion HJB that decomposes naturally into capital and pollution components under power-type value functions. Finally, a formulation in terms of Poisson random measures unifies the dynamics, makes arrivals and compensators explicit, and accommodates state-dependent magnitudes. Together, these results establish rigorous verification theorems, highlight how vulnerability emerges endogenously from the joint evolution of capital and pollution, and show that the prospect of rare, state-dependent disasters fundamentally reshapes optimal intertemporal trade-offs.
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Citation
Daria Sakhanda. "Infinite-Horizon Optimal Control of Jump-Diffusion Models for Pollution-Dependent Disasters." arXiv preprint. 2025-11-17. http://arxiv.org/abs/2511.13568v1
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References
- [1]ResearchCredibility: 9/10Daria Sakhanda. "Infinite-Horizon Optimal Control of Jump-Diffusion Models for Pollution-Dependent Disasters." arXiv.org. November 17, 2025. Accessed November 18, 2025.
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Original Source
This article is based on Infinite-Horizon Optimal Control of Jump-Diffusion Models for Pollution-Dependent Disasters (arXiv.org)
