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

Author

Listed:
  • S. Cerreia-Vioglio
  • M. Kupper
  • F. Maccheroni
  • M. Marinacci
  • N. Vogelpoth

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 is considered. As a leading example, we study in some detail the duality of conditional Lp-spaces. Keywords: Dual pairs, Hahn-Banach Theorem for modules, complete L0-normed modules, automatic continuity

Suggested Citation

  • S. Cerreia-Vioglio & M. Kupper & F. Maccheroni & M. Marinacci & N. Vogelpoth, 2014. "Conditional Lp-spaces and the duality of modules over f-algebras," Working Papers 535, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    • Handle: RePEc:igi:igierp:535
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    References listed on IDEAS

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    1. Hansen, Lars Peter & Richard, Scott F, 1987. "The Role of Conditioning Information in Deducing Testable," Econometrica, Econometric Society, vol. 55(3), pages 587-613, May.
    2. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
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    Cited by:

    1. Simone Cerreia Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Hilbert A-Modules," Working Papers 544, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    2. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "A Market Foundation for Conditional Asset Pricing," Working Papers 566, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

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