# Gauge Invariance, Geometry and Arbitrage

```@article{Vzquez2009GaugeIG,
title={Gauge Invariance, Geometry and Arbitrage},
author={Samuel E. V{\'a}zquez and Simone Farinelli},
journal={Capital Markets: Asset Pricing \& Valuation eJournal},
year={2009}
}```
• Published 20 August 2009
• Mathematics
• Capital Markets: Asset Pricing & Valuation eJournal
In this work, we identify the most general measure of arbitrage for any market model governed by It\^o processes. We show that our arbitrage measure is invariant under changes of num\'{e}raire and equivalent probability. Moreover, such measure has a geometrical interpretation as a gauge connection. The connection has zero curvature if and only if there is no arbitrage. We prove an extension of the Martingale pricing theorem in the case of arbitrage. In our case, the present value of any traded…
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