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Summary: Metrics on the set of semimartingale filtrations
Stefan Ankirchner
Department of Mathematics
Imperial College
London SW7 2AZ
March 6, 2006
Abstract
Let X be a stochastic process with cadlag paths. We consider the
set of all filtrations under which X is a semimartingale, and we define a
distance between such filtrations with the help of the bounded variation
parts in the corresponding decompositions of X. We show that this
distance is a complete metric on the set of semimartingale filtrations if
the given process X is continuous.
2000 AMS subject classifications: primary 21B28, 91B16; secondary
60H30, 94A17.
Key words and phrases: semimartingale; Sp; filtration; complete
metric; information drift.
1 Introduction
Let (Ft) be a filtration on some fixed probability space satisfying the usual
conditions. The vector space of all processes which are semimartingales with
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