Volume 15, 2011
Supplement: In honor of Marc Yor
|Page(s)||S25 - S38|
|Published online||19 May 2011|
Local martingales and filtration shrinkage
Humboldt Universität, Berlin, Germany
2 Supported in part by NSF Grant DMS-0906995; Statistics, Columbia University, New York, NY, 10027, USA
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.
Mathematics Subject Classification: 60G44 / 60H05 / 60J65 / 60J55
Key words: Filtration shrinkage / filtration expansion / martingales / semimartingales / local time / Brownian motion
© EDP Sciences, SMAI, 2011
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