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Common mathematical foundations of expected utility and dual utility theories

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  • Dentcheva, Darinka
  • Ruszczynski, Andrzej

Abstract

We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous linear functionals from functional analysis. Our analysis reveals the dual character of utility functions. We also derive new integral representations of dual utility models.

Suggested Citation

  • Dentcheva, Darinka & Ruszczynski, Andrzej, 2012. "Common mathematical foundations of expected utility and dual utility theories," MPRA Paper 42736, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:42736
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    File URL: https://mpra.ub.uni-muenchen.de/42736/1/MPRA_paper_42736.pdf
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    References listed on IDEAS

    as
    1. Sergei Guriev, 2001. "On Microfoundations of the Dual Theory of Choice," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 26(2), pages 117-137, September.
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    Cited by:

    1. Nilay Noyan & Gábor Rudolf, 2015. "Kusuoka representations of coherent risk measures in general probability spaces," Annals of Operations Research, Springer, vol. 229(1), pages 591-605, June.
    2. Roberto Cominetti & Alfredo Torrico, 2016. "Additive Consistency of Risk Measures and Its Application to Risk-Averse Routing in Networks," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1510-1521, November.
    3. Michel de Lara & Olivier Gossner, 2019. "Payoffs-Beliefs Duality and the Value of Information," Working Papers hal-01941006, HAL.

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    More about this item

    Keywords

    Preferences; Utility Functions; Rank Dependent Utility Functions; Separation; Choquet Representation;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General

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