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filtration shrinkage

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Local martingales and filtration shrinkage
Hans Föllmer, Philip Protter
Journal:

ESAIM: Probability and Statistics / Volume 15 / 2011

Published online by Cambridge University Press:

15 October 2010, pp. S25-S38

Print publication:

2011
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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.