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Utility Representation in Abstract Wiener Space

Author

Listed:
  • Charles-Cadogan, G.

    (University of Leicester)

Abstract
We extend Machina’s (1982) preference functional to abstract Wiener space. This has the advantage of extending utility functions to: infinite dimensional spaces; providing estimates for Machina’s (1982) nonlinear utility functional; and establishing a nexus between microfoundations of local utility, subjective probability, prospect theory, and elements of quantum decision theory without complex valued Hilbert spaces. For example, the class of Markowitz nonconvex utility functions (for which prospect theory’s value function is a special case) are vector valued functions in abstract Wiener space. Instead of preferences over probability distributions, the problem is transformed into one of preferences over states. Under Arzela-Ascoli Theorem, Wiener measure is the limit and unique conjugate prior in Wiener space. By a change of measure local subjective (posterior) probability is a Wiener integral. So, binary choice is stochastic. This poses a challenge for the transitivity axiom because intransitive preferences will occur in that space almost surely. Savage’s (1972) SEU fails in the space because probability is state dependent. JEL codes: C02 ; D81

Suggested Citation

  • Charles-Cadogan, G., 2021. "Utility Representation in Abstract Wiener Space," CRETA Online Discussion Paper Series 70, Centre for Research in Economic Theory and its Applications CRETA.
    • Handle: RePEc:wrk:wcreta:70
    as

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    File URL: https://warwick.ac.uk/fac/soc/economics/research/centres/creta/papers/manage/creta70_-_g_charles-cadogan.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    decision theory ; local utility ; nonlinear subjective probability ; abstract Wiener spaces;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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