Finitely Additive Supermartingales

17 Pages Posted: 16 Jul 2005

See all articles by Gianluca Cassese

Gianluca Cassese

Department of Economics, Statistics and Management; University of Lugano - Institute of Finance

Date Written: February 1, 2006

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

Suggested Citation

Cassese, Gianluca, Finitely Additive Supermartingales (February 1, 2006). Available at SSRN: https://ssrn.com/abstract=756630 or http://dx.doi.org/10.2139/ssrn.756630

Gianluca Cassese (Contact Author)

Department of Economics, Statistics and Management ( email )

Via Bicocca degli Arcimboldi, 8
Milan, MI 20126
Italy

HOME PAGE: http://www.statistica.unimib.it/utenti/cassese

University of Lugano - Institute of Finance ( email )

Via Buffi 13
CH-6900 Lugano
Switzerland

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