On arbitrages arising from honest times

Claudio Fontana, Monique Jeanblanc and Shiqi Song

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Abstract: In the context of a general continuous financial market model, we study whether the additional information associated with an honest time gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations, we explicitly show that no kind of arbitrage profit can ever be realised strictly before an honest time, while classical arbitrage opportunities can be realised exactly at an honest time as well as after an honest time. Moreover, stronger arbitrages of the first kind can only be obtained by trading as soon as an honest time occurs. We carefully study the behavior of local martingale deflators and consider no-arbitrage-type conditions weaker than NFLVR.

Date: 2012-07, Revised 2013-07
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Published in Finance and Stochastics, 2014, vol. 18(3), 515-543

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