Paper: arXiv 2511.03358

Authors: Alexander Alecio

Abstract

We consider a model for systemic risk comprising of a system of diffusion processes, interacting through their empirical mean. Each process is subject to a confining double-well potential with some uncertainty in the coefficients, corresponding to fluctuations in height of the potential barrier seperating the two wells. This is equivalent to studying a single McKean-Vlasov SDE with explicit dependence on its moments and, novelly, independently varying additive and multiplicative noise. Such non-linear SDEs are known to possess two phases: stable (ordered) and unstable (disordered). When the potential is purely bistable, the phase changes from stable to unstable when noise intensity is increased past a critical threshold. With the recent advances, it will be shown that the behaviour here is far richer: indeed, depending on the interpretation of the stochastic integral, the system exhibits phase changes that cannot occur in any regime where there is no uncertainty in the potential. Strikingly, this allows for the phenomenon of noise induced stability; situations where more noise can reduce the risk of system failure.

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 presents a sophisticated theoretical framework analyzing systemic risk via McKean-Vlasov SDEs and stochastic calculus, demonstrating novel phenomena like noise-induced stability under parameter uncertainty. However, it is purely mathematical/theoretical with no real-world financial data validation or backtesting empirical rigor.

Research Flowchart

  flowchart TD
    A[Goal: Analyze Systemic Risk & Noise-Induced Stability] --> B[Input: McKean-Vlasov SDE with Double-Well Potential]
    B --> C[Model Additive & Multiplicative Noise Uncertainty]
    C --> D[Evaluate Stochastic Integrals: Itô vs Stratonovich]
    D --> E[Analyze Phase Transitions: Stable vs Unstable]
    E --> F[Outcome: Richer Phase Changes via Potential Uncertainty]
    E --> G[Outcome: Noise-Induced Stability Reduces Failure Risk]

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0 of 56 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.