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Local martingales and filtration shrinkage

Published online by Cambridge University Press:  15 October 2010

Hans Föllmer  and
Philip Protter
Hans Föllmer
Affiliation:
Humboldt Universität, Berlin, Germany
Philip Protter
Affiliation:
Supported in part by NSF Grant DMS-0906995; Statistics, Columbia University, New York, NY, 10027, USA. [email protected]
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Abstract

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.

Keywords

Filtration shrinkagefiltration expansionmartingalessemimartingaleslocal timeBrownian motion
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 15: Supplement: In honor of Marc Yor , 2011 , pp. S25 - S38
Copyright
© EDP Sciences, SMAI, 2011

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