Arbitrage theory without a numéraire

2014/10/11 by Michael R. Tehranchi, Tehranchi, Michael R.
Economics, Econometrics and Finance · #60G42 #91B25 #Capital Investment and Risk Analysis #Economic theories and models #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1410.2976

openalex publication_date 2014/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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