Systemic Risk Management via Maximum Independent Set in Extremal Dependence Networks

ArXiv ID: 2503.15534 “View on arXiv”

Authors: Unknown

Abstract

The failure of key financial institutions may accelerate risk contagion due to their interconnections within the system. In this paper, we propose a robust portfolio strategy to mitigate systemic risks during extreme events. We use the stock returns of key financial institutions as an indicator of their performance, apply extreme value theory to assess the extremal dependence among stocks of financial institutions, and construct a network model based on a threshold approach that captures extremal dependence. Our analysis reveals different dependence structures in the Chinese and U.S. financial systems. By applying the maximum independent set (MIS) from graph theory, we identify a subset of institutions with minimal extremal dependence, facilitating the construction of diversified portfolios resilient to risk contagion. We also compare the performance of our proposed portfolios with that of the market portfolios in the two economies.

Keywords: Systemic Risk, Extreme Value Theory, Financial Networks, Portfolio Optimization, Risk Contagion

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics, including multivariate regular variation, spectral measures, and graph theory (maximum independent set), which is dense and theoretically rigorous. It also demonstrates empirical rigor by applying the methodology to real-world financial data (Chinese and U.S. stocks), constructing networks, running backtests, and comparing portfolio performance against market benchmarks.

  flowchart TD
    A["Research Goal<br>Mitigate systemic risk contagion among<br>financial institutions during extreme events"]
    B["Data Inputs<br>Historical stock returns<br>for key institutions"]
    C["Methodology Steps<br>1. Extreme Value Theory<br>2. Extremal Dependence Network<br>3. Maximum Independent Set"]
    D["Computational Processes<br>Construct threshold network<br>Calculate extremal correlations<br>Apply MIS algorithm"]
    E["Key Findings & Outcomes<br>Comparative analysis: CN vs US systems<br>Identification of non-overlapping risk clusters<br>Construction of resilient portfolios"]
    
    A --> B
    B --> C
    C --> D
    D --> E