Paper: arXiv 2512.24491

Authors: Graeme Baker, Ankita Chatterjee

Abstract

We consider a reflected process in the positive orthant driven by an exogenous jump process. For a given input process, we show that there exists a unique minimal strong solution to the given particle system up until a certain maximal stopping time, which is stated explicitly in terms of the dual formulation of a linear programming problem associated with the state of the system. We apply this model to study the ruin time of interconnected insurance firms, where the stopping time can be interpreted as the failure time of a reinsurance agreement between the firms. Our work extends the analysis of the particle system in Baker, Hambly, and Jettkant (2025) to the case of jump driving processes, and the existence result of Reiman (1984) beyond the case of sub-stochastic reflection matrices.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical extension of the Skorokhod reflection problem to jump processes using duality in linear programming. While mathematically solid with clear proofs and a brief Monte Carlo illustration, it lacks deep empirical validation or real-world data backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve Skorokhod Reflection Problem<br>driven by jump processes for systemic risk] --> B[Inputs: Exogenous Jump Process &<br>Interconnected System Reflection Matrix]
    B --> C[Methodology: Apply Dual LP Formulation<br>to analyze particle system state]
    C --> D[Computational Process: Extend Reiman '84 &<br>Baker et al. '25 models beyond sub-stochastic limits]
    D --> E[Outcome 1: Prove unique minimal strong solution<br>up to explicit maximal stopping time]
    D --> F[Outcome 2: Model ruin times & reinsurance<br>agreement failure in interconnected firms]

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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.