Local martingales and filtration shrinkage

Hans Föllmer , Philip Protter

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.

Mots clés: Filtration shrinkage; filtration expansion; martingales; semimartingales; local time; Brownian motion

Hans Föllmer, Philip Protter. Local martingales and filtration shrinkage. ESAIM: Probability and Statistics, 2010, 15, pp.S25-S38. ⟨10.1051/ps/2010023⟩. ⟨hal-00632722⟩