Local martingales and filtration shrinkage
ESAIM: Probability and Statistics, Tome 15 (2011), pp. S25-S38.

A general theory is developed for the projection of martingale related processes onto smaller filtrations, to which they are not even adapted. Martingales, supermartingales, and semimartingales retain their nature, but the case of local martingales is more delicate, as illustrated by an explicit case study for the inverse Bessel process. This has implications for the concept of No Free Lunch with Vanishing Risk, in Finance.

DOI : 10.1051/ps/2010023
Classification : 60G44, 60H05, 60J65, 60J55
Mots clés : filtration shrinkage, filtration expansion, martingales, semimartingales, local time, brownian motion 
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Föllmer, Hans; Protter, Philip. Local martingales and filtration shrinkage. ESAIM: Probability and Statistics, Tome 15 (2011), pp. S25-S38. doi : 10.1051/ps/2010023. http://www.numdam.org/articles/10.1051/ps/2010023/

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