Finitely Additive Supermartingales

Abstract

Finitely additive supermartingale, a concept originally due to Bochner, is revived to study measure decompositions over filtered probability spaces. We obtain versions of the Doob Meyer decomposition for finitely additive and classical supermartingales in a rather general context. Also we obtain a characterization of finitely additive expectation based on a generalization of conditional expectation to finitely additive measures.

Keywords: Conditional expectation, Doleans-Dade measure, Doob Meyer decomposition, finitely additive measures, finitely additive supermartingales, potential, supermartingales, Yosida Hewitt decomposition

JEL Classification: C60, C61, G12