Deterministic Criteria for the Absence and Existence of Arbitrage in Multi-Dimensional Diffusion Markets

TL;DR

This paper establishes deterministic conditions to determine when arbitrage opportunities exist or are absent in multi-dimensional diffusion markets, highlighting differences between classical no-arbitrage conditions.

Contribution

It introduces new deterministic criteria for arbitrage existence and non-existence in complex diffusion-driven markets, enabling tailored market constructions.

Findings

Criteria for absence of arbitrage in multi-dimensional diffusions

Markets can satisfy no unbounded profit with bounded risk but violate no free lunch with vanishing risk

Provides tools for constructing markets with specific arbitrage properties

Abstract

We derive deterministic criteria for the existence and non-existence of equivalent (local) martingale measures for financial markets driven by multi-dimensional time-inhomogeneous diffusions. Our conditions can be used to construct financial markets in which the \emph{no unbounded profit with bounded risk} condition holds, while the classical \emph{no free lunch with vanishing risk} condition fails.