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Arbitrage theory without a num\'eraire

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  • Michael R. Tehranchi

Abstract

This note develops an arbitrage theory for a discrete-time market model without the assumption of the existence of a num\'eraire 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.

Suggested Citation

  • Michael R. Tehranchi, 2014. "Arbitrage theory without a num\'eraire," Papers 1410.2976, arXiv.org, revised Jul 2015.
    • Handle: RePEc:arx:papers:1410.2976
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    References listed on IDEAS

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    5. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
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    Cited by:

    1. Bálint, Dániel Ágoston, 2022. "Characterisation of L0-boundedness for a general set of processes with no strictly positive element," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 51-75.

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