Paper: arXiv 2511.13568

Authors: Daria Sakhanda, Joshué Helí Ricalde-Guerrero

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly sophisticated theoretical framework using jump-diffusion control processes, Poisson random measures, and non-local HJB equations to model environmental disaster risks. However, it is purely theoretical and completely lacks empirical validation, empirical data, or backtesting components.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Stochastic Growth & Pollution-Dependent Disaster Risk] --> B[Inputs: Capital, Pollution Accumulation, & Endogenous Jump Parameters]
    B --> C[Methodology: Poisson Point Process & Jump-Diffusion Control Framework]
    C --> D[Computational Process: Derive Non-Local HJB Equation]
    D --> E[Computational Process: Value Function Decomposition & Closed-Form Solutions]
    E --> F[Key Findings: Composite State Variable for Risk Exposure & Optimized Pollution Abatement]

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0 of 34 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.