Random expected utility theory with a continuum of prizes

Collection Location Koleksi E-book & E-Journal Perpustakaan Pusat Unila
Edition vol.271issue 2
Call Number
ISBN/ISSN 15729338
Author(s) Ma, Wei
Subject(s) Business and Management
Classification NONE
Series Title
GMD E-Journal
Publisher Springer
Publishing Year 2018
Publishing Place Switzerland
Abstract/Notes Abstract This note generalizes Gul and Pesendorfer’s random expected utility theory, a stochastic reformulation of von Neumann–Morgenstern expected utility theory for lotteries overafinitesetofprizes,tothecircumstanceswithacontinuumofprizes.Let[0, M]denote thiscontinuumofprizes;assumethateachutilityfunctioniscontinuous,letC0[0, M]bethe set of all utility functions which vanish at the origin, and define a random utility function to be a finitely additive probability measure on C0[0, M] (associated with an appropriate algebra).Itisshownherethatarandomchoiceruleismixturecontinuous,monotone,linear, and extreme if, and only if, the random choice rule maximizes some regular random utility function. To obtain countable additivity of the random utility function, we further restrict ourconsiderationtothoseutilityfunctionsthatarecontinuouslydifferentiableon[0, M]and vanish at zero. With this restriction, it is shown that a random choice rule is continuous, monotone, linear, and extreme if, and only if, it maximizes some regular, countably additive random utility function. This generalization enables us to make a discussion of risk aversion in the framework of random expected utility theory. Keywords Expected utility·Random utility·Random choice·Independence axiom·Risk aversion
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