Paper: arXiv 2505.18448

Authors: Yucheng Guo, Qinxin Yan

Abstract

We introduce a family of particle systems on sparse graphs where local interactions occur via hitting times, providing a dynamic and tractable model for default cascades in large sparsely-connected financial networks. Building on the framework of Lacker, Ramanan and Wu (2023), we extend convergence theory to systems with singular interactions, capturing the abrupt and discontinuous nature of systemic events. We establish conditions for well-posedness through a minimality principle and connect fragility to dynamic percolation thresholds. Our analysis demonstrates continuity of the joint law of defaults with respect to local graph convergence, establishes convergence of empirical distributions, and characterizes the default time distribution in tree-like networks. This framework offers a rigorous and flexible foundation for modeling systemic risk in evolving financial systems, featuring continuous-time dynamics, heterogeneous and local interactions, and instantaneous default cascades.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a highly sophisticated theoretical framework extending interacting particle systems and dynamic percolation to financial default cascades on graphs. However, it is purely mathematical probability/stochastic analysis with zero empirical data or backtesting included in the excerpt.

Research Flowchart

  flowchart TD
    A[Research Goal: Model systemic default cascades via particle systems on sparse graphs] --> B[Inputs: Graph topology & continuous-time local hitting time interactions]
    B --> C[Methodology: Extend Lacker-Ramanan-Wu framework to singular local interactions]
    C --> D[Analysis: Establish well-posedness via minimality & dynamic percolation thresholds]
    D --> E[Key Finding: Prove continuity of default laws & convergence of empirical distributions]
    D --> F[Key Finding: Characterize exact default time distributions on tree-like networks]

Cited References (40)

  1. Systemic Risk in Financial Systems (2001)
  2. Local weak convergence for sparse networks of interacting processes (2023) — link
  3. Marginal dynamics of interacting diffusions on unimodular Galton–Watson trees (2023)
  4. Systemic risk in financial systems (2001)
  5. Contagion in financial networks (2010)
  6. How likely is contagion in financial networks? (2015)
  7. Systemic risk and stability in financial networks (2015)
  8. DebtRank: Too central to fail? Financial networks, the FED and systemic risk (2012)
and 32 more
  1. Mean field games and systemic risk (2015)
  2. Systemic risk mitigation in financial networks (2015)
  3. Mean field games via controlled martingale problems: Existence of Markovian equilibria (2016)
  4. Global solvability of a networked integrate-and-fire model of McKean-Vlasov type (2015)
  5. Propagation of minimality in the supercooled Stefan problem (2023) — link
  6. Resilience to contagion in financial networks (2016)
  7. Lecture notes on random graphs and probabilistic combinatorial optimization (2016)
  8. Percolation (1999) — link
  9. Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues (2002)
  10. Stochastic Calculus for Finance II: Continuous-Time Models (2004) — link
  11. Random Graphs and Complex Networks (2024)
  12. McKean-Vlasov equations with positive feedback through elastic stopping times (2022) — link
  13. An SPDE model for systemic risk with endogenous contagion (2019) — link
  14. Mean field games with absorption and common noise with a model of bank run (2023) — link
  15. Network Effects in Default Clustering for Large Systems (2019) — link
  16. Mean-Field Limit of a Stochastic Particle System Smoothly Interacting Through Threshold Hitting-Times and Applications to Neural Networks with Dendritic Component (2015)
  17. Network Structure and Systemic Risk in Banking Systems (2013)
  18. Particle systems with a singular mean-field self-excitation. Application to neuronal networks (2015) — link
  19. Global Solution to Super-cooled S tefan Problem with Blow-ups: Regularity and Uniqueness (2022)
  20. Mean field systems on networks, with singular interaction through hitting times (2020) — link
  21. Particle Systems and McKean–Vlasov Dynamics with Singular Interaction through Local Times (2025) — link
  22. Contagious McKean–Vlasov problems with common noise: from smooth to singular feedback through hitting times (2023) — link
  23. Control of McKean–Vlasov SDEs with Contagion Through Killing at a State-Dependent Intensity (2023) — link
  24. The supercooled Stefan problem with transport noise: weak solutions and blow-up (2024) — link
  25. A singular two-phase Stefan problem and particles interacting through their hitting times (2024) — link
  26. Optimal bailout strategies resulting from the drift controlled supercooled Stefan problem (2024) — link
  27. Systemic Robustness: A Mean-Field Particle System Approach (2025) — link
  28. Stefan Problem with Surface Tension: Uniqueness of Physical Solutions under Radial Symmetry (2024) — link
  29. Cascade equation for the discontinuities in the Stefan problem with surface tension (2024) — link
  30. Contagious McKean–Vlasov systems with heterogeneous impact and exposure (2023) — link
  31. Network topology of the interbank market (2004) — link
  32. Interbank tiering and money center banks (2014) — link

0 of 40 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.