Paper: arXiv 2406.19242

Authors: Corrado De Vecchi, Max Nendel, Jan Streicher

Abstract

In this paper, we study dependence uncertainty and the resulting effects on tail risk measures, which play a fundamental role in modern risk management. We introduce the notion of a regular dependence measure, defined on multi-marginal couplings, as a generalization of well-known correlation statistics such as the Pearson correlation. The first main result states that even an arbitrarily small positive dependence between losses can result in perfectly correlated tails beyond a certain threshold and seemingly complete independence before this threshold. In a second step, we focus on the aggregation of individual risks with known marginal distributions by means of arbitrary nondecreasing left-continuous aggregation functions. In this context, we show that under an arbitrarily small positive dependence, the tail risk of the aggregate loss might coincide with the one of perfectly correlated losses. A similar result is derived for expectiles under mild conditions. In a last step, we discuss our results in the context of credit risk, analyzing the potential effects on the value at risk for weighted sums of Bernoulli distributed losses.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides strong mathematical rigor in the field of quantitative risk management by defining regular dependence measures and proving worst-case tail risk behavior under dependence uncertainty. However, it is fundamentally a theoretical paper with limited empirical validation, relying primarily on stylized numerical examples rather than real-world datasets.

Research Flowchart

  flowchart TD
    A[Research Goal: Evaluate Tail Risk Under Dependence Uncertainty] --> B[Inputs: Known Marginals & Aggregation Functions]
    B --> C[Define Regular Dependence Measure]
    C --> D[Analyze Tail Risk Behavior & Expectiles]
    D --> E[Apply to Credit Risk Model: Weighted Bernoulli Losses]
    E --> F[Key Outcome: Minimal Dependence Can Trigger Perfect Tail Correlation & Worst-Case VaR]

Cited References (52)

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2 of 52 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.