Deterministic criteria for the absence of arbitrage in one-dimensional diffusion models

TL;DR

This paper provides a deterministic characterization of various no-arbitrage conditions in one-dimensional diffusion models, clarifying their relationships and implications in financial mathematics.

Contribution

It introduces a unified deterministic framework for understanding no-arbitrage conditions in one-dimensional diffusion models, linking different notions of arbitrage.

Findings

Unified deterministic criteria for no-arbitrage conditions

Clarified relationships among different no-arbitrage notions

Applicable to one-dimensional diffusion financial models

Abstract

We obtain a deterministic characterisation of the \emph{no free lunch with vanishing risk}, the \emph{no generalised arbitrage} and the \emph{no relative arbitrage} conditions in the one-dimensional diffusion setting and examine how these notions of no-arbitrage relate to each other.