Risk-Consistent Conditional Systemic Risk Measures

TL;DR

This paper introduces a new class of risk measures for systemic risk that are conditionally defined and can be decomposed into simpler components, extending existing unconditional risk measure results.

Contribution

It develops a risk-consistent conditional systemic risk measure framework on general probability spaces, unifying various existing measures and extending theoretical understanding.

Findings

Framework covers many practical systemic risk measures

Extends known results from unconditional to conditional risk measures

Applicable on general probability spaces

Abstract

We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional aggregation and a univariate conditional risk measure. Our studies extend known results for unconditional risk measures on finite state spaces. We argue in favor of a conditional framework on general probability spaces for assessing systemic risk. Mathematically, the problem reduces to selecting a realization of a random field with suitable properties. Moreover, our approach covers many prominent examples of systemic risk measures from the literature and used in practice.