Motivated by dynamic asset pricing, we extend the dual pairs’ theory of Dieudonné (1942) and Mackey (1945) to pairs of modules over a Dedekind complete f-algebra with multiplicative unit. The main tools are: - a Hahn–Banach Theorem for modules of this kind; - a topology on the f-algebra that has the special feature of coinciding with the norm topology when the algebra is a Banach algebra and with the strong order topology of Filipovic, Kupper, and Vogelpoth (2009), when the algebra of all random variables on a probability space (Ω, G, P) is considered. As a leading example, we study in some detail the duality of conditional Lp-spaces.

Conditional Lp-spaces and the duality of modules over f-algebras

CERREIA VIOGLIO, SIMONE;MACCHERONI, FABIO ANGELO;MARINACCI, MASSIMO;
2016

Abstract

Motivated by dynamic asset pricing, we extend the dual pairs’ theory of Dieudonné (1942) and Mackey (1945) to pairs of modules over a Dedekind complete f-algebra with multiplicative unit. The main tools are: - a Hahn–Banach Theorem for modules of this kind; - a topology on the f-algebra that has the special feature of coinciding with the norm topology when the algebra is a Banach algebra and with the strong order topology of Filipovic, Kupper, and Vogelpoth (2009), when the algebra of all random variables on a probability space (Ω, G, P) is considered. As a leading example, we study in some detail the duality of conditional Lp-spaces.
2016
CERREIA VIOGLIO, Simone; Kupper, Michael; Maccheroni, FABIO ANGELO; Marinacci, Massimo; Vogelpoth, Nicolas
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11565/3995432
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