Arbitrage and Hedging in a non probabilistic framework

TL;DR

This paper explores hedging and arbitrage without relying on probability, using topological methods to analyze trajectory spaces and connect with traditional probabilistic models, especially those beyond semimartingales.

Contribution

It introduces conditions for non probabilistic arbitrage based on topology and links these to classical notions, with applications to advanced financial models.

Findings

Conditions for non probabilistic arbitrage established

Examples of perfect option replication under various trajectories

Applications to models beyond semimartingales

Abstract

The paper studies the concepts of hedging and arbitrage in a non probabilistic framework. It provides conditions for non probabilistic arbitrage based on the topological structure of the trajectory space and makes connections with the usual notion of arbitrage. Several examples illustrate the non probabilistic arbitrage as well perfect replication of options under continuous and discontinuous trajectories, the results can then be applied in probabilistic models path by path. The approach is related to recent financial models that go beyond semimartingales, we remark on some of these connections and provide applications of our results to some of these models.