Doob’s decomposition of set-valued submartingales via ordered near vector spaces

  • Coenraad CA Labuschagne
  • Andrew L Pinchuck

Abstract

We use ideas from measure-free martingale theory and R˚adstr¨om’ completion of a near vector space to derive a Doob decomposition of submartingales in ordered near vector spaces. As a special cases thereof, we obtain the Doob decomposition of set-valued submartingales, as noted by Daures, Ni and Zhang, and an analogue of the Doob decomposition of set-valued submartingales, as noted by Shen and Wang.

Quaestiones Mathematicae 32(2009), 247–264

Author Biographies

Coenraad CA Labuschagne
Programme in Advanced Mathematics of Finance, Department of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, 2050 WITS, South Africa
Andrew L Pinchuck
Department of Mathematics, Rhodes University, P.O. Box 94, Grahamstown, 6140, South Africa
Section
Articles

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606