Paper: arXiv 2411.09657

Authors: Fan Yang, Yi Zhang

Abstract

We study the tail asymptotics of the sum of two heavy-tailed random variables. The dependence structure is modeled by copulas with the so-called tail order property. Examples are presented to illustrate the approach. Further for each example we apply the main results to obtain the asymptotic expansions for Value-at-Risk of aggregate risk.

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 rigorous mathematical derivations of second-order tail asymptotics for heavy-tailed sum risks using copulas with tail order properties. While mathematically advanced and theoretical novel, it lacks empirical backtesting and relies primarily on analytical proofs and asymptotic approximations.

Research Flowchart

  flowchart TD
    A[Research Goal: Tail Asymptotics of Aggregate Heavy-Tailed Risks] --> B[Inputs: Two Heavy-Tailed RVs & Copulas with Tail Order Property]
    B --> C[Methodology: Derive Asymptotic Expansions for Risk Sums]
    C --> D[Computational Process: Apply Main Results to Specific Copula Models]
    D --> E[Outcome: Value-at-Risk VaR Expansions for Multi-Asset Portfolios]

Cited References (37)

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  2. Sharp asymptotics for large portfolio losses under extreme risks (2019) — link
  3. Modeling multivariate ocean data using asymmetric copulas (2018) — link
  4. Estimation of tail risk based on extreme expectiles (2016) — link
  5. Risk concentration based on Expectiles for extreme risks under FGM copula (2015) — link
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  7. Estimation of the marginal expected shortfall: the mean when a related variable is extreme (2012) — link
  8. Second order tail asymptotics for the sum of dependent, tail-independent regularly varying risks (2012) — link
and 29 more
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  3. Extreme residual dependence for random vectors and processes (2011) — link
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0 of 37 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.