Paper: arXiv 2410.00158

Authors: Bingzhen Geng, Yang Liu, Hongfu Wan

Abstract

Systemic risk is receiving increasing attention in the insurance industry. In this paper, we propose a multi-dimensional Lévy process-based renewal risk model with heterogeneous insurance claims, where every dimension indicates a business line of an insurer. We use the systemic expected shortfall (SES) and marginal expected shortfall (MES) defined with a Value-at-Risk (VaR) target level as the measurement of systemic risk. Assuming that all the claim sizes are pairwise asymptotically independent (PAI), we derive asymptotic formulas for the tail probabilities of discounted aggregate claims and the total loss, which hold uniformly for all time horizons. We further obtain the asymptotics of the above systemic risk measures. The main technical issues involve the treatment of uniform convergence in the dynamic time setting. Finally, we perform a detailed Monte Carlo study to validate our asymptotics and analyze the impact and sensitivity of key parameters in the asymptotic expressions both analytically and numerically.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides rigorous mathematical derivations for asymptotic systemic risk measures (SES and MES) in a multi-dimensional renewal model driven by Lévy processes and heavy-tailed claim distributions. While it includes a Monte Carlo simulation study to validate theoretical results, it lacks empirical backtesting or real-world financial data application, placing it squarely in the theoretical domain.

Research Flowchart

  flowchart TD
    A[Goal: Analyze Systemic Risk Asymptotics in Multi-Line Insurance] --> B[Model & Inputs: Multi-Dimensional Lévy Renewal Model + PAI Claim Sizes]
    B --> C[Derive Uniform Asymptotics for Discounted Aggregate Claims & Total Loss]
    C --> D[Technical Challenge: Resolve Uniform Convergence in Dynamic Time Setting]
    D --> E[Calculate Systemic Risk Measures: SES & MES via VaR]
    E --> F[Validate Results & Perform Parameter Sensitivity via Monte Carlo Simulations]
    F --> G[Outcomes: Explicit Asymptotic Formulas for SES/MES & Parameter Insights]

Cited References (34)

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1 of 34 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.