# Dual representations for systemic risk measures based on acceptance sets

## TL;DR

This paper develops dual representations for systemic risk measures using acceptance sets, covering different allocation-aggregation approaches and providing insights into their structure and duality properties.

## Contribution

It introduces a unified dual representation framework for systemic risk measures based on acceptance sets, applicable to various allocation and aggregation schemes.

## Key findings

- Dual representations for systemic risk measures are established.
- Analysis of systemic acceptance sets and their support functions.
- Simplified proof of duality for utility-based univariate risk measures.

## Abstract

We establish dual representations for systemic risk measures based on acceptance sets in a general setting. We deal with systemic risk measures of both "first allocate, then aggregate" and "first aggregate, then allocate" type. In both cases, we provide a detailed analysis of the corresponding systemic acceptance sets and their support functions. The same approach delivers a simple and self-contained proof of the dual representation of utility-based risk measures for univariate positions.