Set-valued intrinsic measures of systemic risk

Paper: arXiv 2311.14588

Authors: Jana Hlavinova, Birgit Rudloff, Alexander Smirnow

Abstract

In recent years, it has become apparent that an isolated microprudential approach to capital adequacy requirements of individual institutions is insufficient. It can increase the homogeneity of the financial system and ultimately the cost to society. For this reason, the focus of the financial and mathematical literature has shifted towards the macroprudential regulation of the financial network as a whole. In particular, systemic risk measures have been discussed as a risk measurement and mitigation tool. In this spirit, we adopt a general approach of multivariate, set-valued risk measures and combine it with the notion of intrinsic risk measures. In order to define the risk of a financial position, intrinsic risk measures utilise only internal capital, which is received when part of the currently held assets are sold, instead of relying on external capital. We translate this methodology into the systemic framework and show that systemic intrinsic risk measures have desirable properties such as the set-valued equivalents of monotonicity and quasi-convexity. Furthermore, for convex acceptance sets we derive a dual representation of the systemic intrinsic risk measure. We apply our methodology to a modified Eisenberg-Noe network of banks and discuss the appeal of this approach from a regulatory perspective, as it does not elevate the financial system with external capital. We show evidence that this approach allows to mitigate systemic risk by moving the network towards more stable assets.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a highly sophisticated mathematical extension of systemic risk measures using set-valued analysis, quasi-convexity, and dual representations. However, it relies heavily on theoretical formulations and a stylized network simulation (modified Eisenberg-Noe) rather than rigorous empirical validation on real-world financial data.

Research Flowchart

  flowchart TD
    A[Research Goal: Develop macroprudential systemic risk measures using internal capital] --> B[Framework Integration: Set-valued multivariate risk measures + Intrinsic risk measures]
    B --> C[Inputs: Financial network data & Asset portfolios]
    C --> D[Model Application: Modified Eisenberg-Noe network with cross-asset sales]
    D --> E[Mathematical Analysis: Prove monotonicity, quasi-convexity & derive dual representation]
    E --> F[Key Outcomes: Mitigates systemic risk via internal capital reallocation & shifts network to stable assets]

Cited References (22)

1. The joint impact of bankruptcy costs, fire sales and cross-holdings on systemic risk in financial networks (2017) — link
2. An analysis of the literature on systemic financial risk: A survey (2017) — link
3. Intrinsic Risk Measures (2016) — link
4. Dual representations for systemic risk measures (2016) — link
5. Contagion! Systemic Risk in Financial Networks (2016) — link
6. Financial contagion and asset liquidation strategies (2015) — link
7. Measures of Systemic Risk (2015) — link
8. Measuring risk with multiple eligible assets (2013) — link

0 of 22 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.