Arbitrage theory without a num\'eraire
Mathematical Finance
2015-07-07 v2
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.
Cite
@article{arxiv.1410.2976,
title = {Arbitrage theory without a num\'eraire},
author = {Michael R. Tehranchi},
journal= {arXiv preprint arXiv:1410.2976},
year = {2015}
}
Comments
27 pages