Weak and strong no-arbitrage conditions for continuous financial markets

TL;DR

This paper provides a comprehensive analysis of various no-arbitrage conditions in continuous financial markets, linking their validity to the properties of asset price processes and martingale deflators, including weaker conditions than classical ones.

Contribution

It offers a unified framework characterizing a spectrum of no-arbitrage conditions and their relation to market models based on continuous semimartingales.

Findings

Complete characterization of no-arbitrage conditions

Link between no-arbitrage and martingale deflators

Review of classical and recent results

Abstract

We propose a unified analysis of a whole spectrum of no-arbitrage conditions for financial market models based on continuous semimartingales. In particular, we focus on no-arbitrage conditions weaker than the classical notions of No Arbitrage and No Free Lunch with Vanishing Risk. We provide a complete characterisation of the considered no-arbitrage conditions, linking their validity to the characteristics of the discounted asset price process and to the existence and the properties of (weak) martingale deflators, and review classical as well as recent results.