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Utility Representation in Abstract Wiener Space

G. Charles-Cadogan
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G. Charles-Cadogan: University of Leicester

CRETA Online Discussion Paper Series from Centre for Research in Economic Theory and its Applications CRETA

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

Keywords: decision theory; local utility; nonlinear subjective probability; abstract Wiener spaces (search for similar items in EconPapers)
Date: 2021
New Economics Papers: this item is included in nep-dcm, nep-ore and nep-upt
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