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Arbitrage theory without a numéraire

This note develops an arbitrage theory for a discrete-time market model without the assumption of the existence of a numéraire asset. Fundamental theorems of asset pricing are stated and proven in this context. The distinction between the notions of investment-consumption arbitrage and pure-investment arbitrage provide a discrete-time analogue of the distinction between the notions of absolute arbitrage and relative arbitrage in the continuous-time theory. Applications to the modelling of bubbles is discussed.

preprint2015arXivOpen access
Michael R. Tehranchi
q-fin.MF
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Michael R. Tehranchi

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