{
  "abstract": "This paper is devoted to developing a framework for stochastic growth models with environmental risk, in which rare but catastrophic shocks interact with capital accumulation and pollution. Building on the Poisson point process formulation studied in arXiv:2511.13568, we extend the model to disasters driven by a marked Hawkes process, allowing past disasters to temporarily increase the likelihood of subsequent shocks. Our work focuses on a subcritical Markovian Hawkes specification, in which the state space is augmented by the self-excitation component of disaster risk. We establish the well-posedness and nonexplosion of the resulting controlled Hawkes dynamics. Using the Hamilton-Jacobi-Bellman characterization of the corresponding Poisson control problem, we obtain quantitative estimates for the Hawkes excitation process and prove, under a small-excitation scaling, that the Hawkes value function converges to its Poisson counterpart as the magnitude of self-excitation vanishes. This provides a rigorous Poisson approximation of the stochastic control problem and quantifies the effect of self-excitation on optimal growth under environmental disaster risk.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29473",
  "author_total": 2,
  "authors": [
    {
      "name": "Daria Sakhanda"
    },
    {
      "name": "Joshué Helí Ricalde-Guerrero"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/axfchfy0sdcbx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29473",
  "fulltext_url": null,
  "id": "axfchfy0sdcbx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29473",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "q-fin.MF"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7204966210",
  "pdf_url": "https://arxiv.org/pdf/2608.29473",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/axfchfy0sdcbx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29473",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29473"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Stochastic Optimal Control of Hawkes Jump-Diffusion Systems",
  "title_text": "Stochastic Optimal Control of Hawkes Jump-Diffusion Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/axfchfy0sdcbx",
  "venue": "arXiv",
  "versions": []
}