A compactness principle for bounded sequences of martingales with applications

Freddy Delbaen, Walter Schachermayer

Publikation: Working/Discussion PaperWU Working Paper

Abstract

For H^1 bounded sequences, we introduce a technique, related to the Kadec-Pelczynski -decomposition for L^1 sequences, that allows us to prove compactness theorems. Roughly speaking, a bounded sequence in H^1 can be split into two sequences, one of which is weakly compact, the other forms the singular part. If the martingales are continuous then the singular part tends to zero in the semi-martingale topology. In the general case the singular parts give rise to a process of bounded variation. The technique allows to give a new proof of the optional decomposition theorem in Mathematical Finance. (author's abstract)
OriginalspracheEnglisch
ErscheinungsortVienna
HerausgeberSFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business
PublikationsstatusVeröffentlicht - 1999

Publikationsreihe

NameReport Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
Nr.23

WU Working Paper Reihe

  • Report Series SFB \Adaptive Information Systems and Modelling in Economics and Management Science\

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