Paper: arXiv 2609.02535

Authors: Alejandro Rodriguez Dominguez

Abstract

This paper develops uniform inference and certified capacity decisions for an estimated financial stability boundary. Conditional risk, temporary cross-impact, and effective risk-bearing capacity are jointly estimated from dependent observations. Conventional pointwise inference is reliable at a separated simple spectral root but can fail near semisimple or defective collisions. Projecting a valid joint confidence region for the underlying inputs avoids this local approximation and yields a three-way regime decision with abstention and a one-sided capacity bound. A verified two-dimensional implementation keeps numerical error from creating a resolved sign. Structural simulations recover the predicted tradeoff between coverage and resolution, while observed-risk stresses distinguish statistical abstention from an insufficient computational budget. The financial conclusions remain conditional on the identification of cross-impact, the normalization of capacity, and stability of the inputs over the action horizon.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a highly mathematical framework for uniform inference at financial stability boundaries, addressing complex spectral nonregularity. While it includes structural simulations and observed-risk stresses, the empirical section described appears to be more illustrative than extensive, focusing on validating the theoretical framework rather than broad market backtesting. The novelty lies in its rigorous statistical treatment of non-regular spectral behavior in financial stability analysis.

Research Flowchart

  flowchart TD
    A[Research Goal: Uniform Inference & Certified Capacity at Stability Boundary] --> B{Methodology: Joint Estimation & Uniform Inference};
    B --> C{Inputs: Dependent Observations of Risk & Impact};
    C --> D[Computational Process: Project Joint Confidence Region & Verification];
    D --> E{Outcome: Three-Way Regime Decision & One-Sided Capacity Bound};
    E --> F[Findings: Tradeoff Coverage/Resolution, Statistical Abstention vs. Insufficient Budget];
    F --> G[Limitations: Conditional on Cross-Impact ID, Capacity Normalization, Input Stability];