{"ID":2840697,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.13568","arxiv_id":"2511.13568","title":"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.","short_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)...","url_abs":"https://arxiv.org/abs/2511.13568","url_pdf":"https://arxiv.org/pdf/2511.13568v3","authors":"[\"Daria Sakhanda\",\"Joshué Helí Ricalde-Guerrero\"]","published":"2025-11-17T16:37:10Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"q-fin.MF\"]","methods":"[\"Diffusion Model\",\"Large Language Model\"]","has_code":false}