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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2511.13568 |
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| _version_ | 1866918422469672960 |
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| author | Sakhanda, Daria Ricalde-Guerrero, Joshué Helí |
| author_facet | Sakhanda, Daria Ricalde-Guerrero, Joshué Helí |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13568 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite-Horizon Optimal Control of Jump-Diffusion Models for Pollution-Dependent Disasters Sakhanda, Daria Ricalde-Guerrero, Joshué Helí Optimization and Control Mathematical Finance 93E20, 60G55, 91-10 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. |
| title | Infinite-Horizon Optimal Control of Jump-Diffusion Models for Pollution-Dependent Disasters |
| topic | Optimization and Control Mathematical Finance 93E20, 60G55, 91-10 |
| url | https://arxiv.org/abs/2511.13568 |