# No-arbitrage with multiple-priors in discrete time

## TL;DR

This paper introduces a new characterization of quasi-sure no-arbitrage in discrete-time models with multiple priors, unifying various existing notions and facilitating key results in mathematical finance.

## Contribution

It provides a novel equivalence for quasi-sure no-arbitrage, connecting it with other conditions and illustrating with explicit examples.

## Key findings

- New characterization of quasi-sure no-arbitrage
- Equivalence with existing no-arbitrage notions
- Illustrative examples demonstrating concepts

## Abstract

In a discrete time and multiple-priors setting, we propose a new characterisation of the condition of quasi-sure no-arbitrage which has become a standard assumption. This characterisation shows that it is indeed a well-chosen condition being equivalent to several previously used alternative notions of no-arbitrage and allowing the proof of important results in mathematical finance. We also revisit the so-called geometric and quantitative no-arbitrage conditions and explicit two important examples where all these concepts are illustrated.