# Model Spaces for Risk Measures

## TL;DR

This paper explores how model-free risk measures imply an underlying probability structure and constructs their maximal domain considering liquidity effects and ambiguity, linking measure properties to domain structure.

## Contribution

It introduces a method to extend model-free risk measures to their maximal domain, incorporating liquidity effects and ambiguity considerations.

## Key findings

- Risk measures imply an underlying probability structure.
- Construction of maximal domain respecting ambiguity profile.
- Analysis of properties and subdifferentiability of risk measures.

## Abstract

We show how risk measures originally defined in a model free framework in terms of acceptance sets and reference assets imply a meaningful underlying probability structure. Hereafter we construct a maximal domain of definition of the risk measure respecting the underlying ambiguity profile. We particularly emphasise liquidity effects and discuss the correspondence between properties of the risk measure and the structure of this domain as well as subdifferentiability properties. Keywords: Model free risk assessment, extension of risk measures, continuity properties of risk measures, subgradients.