Scalar systemic risk measures and Aumann-Shapley allocations

TL;DR

This paper develops a unified framework for scalar systemic risk measures, compares two main approaches, and introduces an Aumann-Shapley inspired capital allocation rule to facilitate systemic capital allocation analysis.

Contribution

It introduces a comprehensive framework that encompasses both aggregate and inject capital approaches to systemic risk, and proposes a novel Aumann-Shapley based capital allocation rule.

Findings

Most inject capital systemic risk measures have axiomatic representations.

The Aumann-Shapley inspired CAR allows for approach-independent systemic capital allocations.

The framework enables comparison and identification of commonalities between different systemic risk measurement methods.

Abstract

We study two different contributions to the theory of (scalar) systemic risk measures. Namely the first aggregate or axiomatic approach and the first inject capital approach. For this purpose we establish a general framework, which is rich enough to embed both approaches. It turns out that in most relevant situations systemic risk measures of the first inject capital approach have a representation in the more general axiomatic approach. Moreover, we study capital allocation rules (CARs). In both situations there exist canonical ways to answer the capital allocation problem. Additionally, a capital allocation rule (CAR) in the spirit of Aumann-Shapley is introduced, which gives us the opportunity to compute systemic capital allocations regardless of the risk measurement approach. This CAR also serves as an instrument to compare both approaches and to identify commonalities.