Conditional Systemic Risk Measures

TL;DR

This paper extends static systemic risk measures to a conditional setting, providing dual representations, explicit formulas for exponential preferences, and interpretations of risk allocations as equilibria.

Contribution

It introduces a general framework for conditional systemic risk measures, including dual representations and explicit formulas, with applications to exponential preferences and equilibrium interpretations.

Findings

Dual representation of conditional systemic risk measures

Explicit formulas for exponential preferences

Interpretation of risk allocations as equilibria

Abstract

We investigate to which extent the relevant features of (static) Systemic Risk Measures can be extended to a conditional setting. After providing a general dual representation result, we analyze in greater detail Conditional Shortfall Systemic Risk Measures. In the particular case of exponential preferences, we provide explicit formulas that also allow us to show a time consistency property. Finally, we provide an interpretation of the allocations associated to Conditional Shortfall Systemic Risk Measures as suitably defined equilibria. Conceptually, the generalization from static to conditional Systemic Risk Measures can be achieved in a natural way, even though the proofs become more technical than in the unconditional framework.