Finitely Additive Supermartingales
17 Pages Posted: 16 Jul 2005
Date Written: February 1, 2006
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
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