A simple proof of Kramkov's result on uniform supermartingale decompositions

Abstract

We give a simple proof of Kramkov's uniform optional decomposition in the case where the class of density processes satisfies a suitable closure property. In this case, the decomposition is previsible.

Keywords:

• uniform supermartingale
• uniform optional decomposition
• uniform predictable decomposition

AMS Subject Classification::

• 60G15

Acknowledgements

I am most grateful to an anonymous referee for pointing out an error in an earlier draft of this paper and for very helpful comments on the presentation. I also thank Sigurd Assing for helpful suggestions and comments.