Asymptotic Theory Of Stochastic Choice Functionals For Prospects With Embedded Comotonic Probability Measures

Godfrey Cadogan

MPRA Paper from University Library of Munich, Germany

Abstract: We introduce a monotone class theory of Prospect Theory's value functions, which shows that they can be replaced almost surely by a topological lifting comprised of a class of compact isomorphic maps that embed weakly co-monotonic probability measures, attached to state space, in outcome space. Thus, agents solve a signal extraction problem to obtain estimates of empirical probability weights for prospects under risk and uncertainty. By virtue of the topological lifting, we prove an almost sure isomorphism theorem between compact stochastic choice operators, and well defined outcomes which, under Brouwer-Schauder theory, guarantees fixed point convergence in convex choice sets. Along the way we introduce a risk operator in the Hoffman-Jorgensen class of lifting operators, and value function [averaging] operators with respect to Radon measure. In that set up, suitable binary operations on gain-loss space show that our risk operator is isometric for gains and skewed for losses. The point spectrum from this operator constitutes the range of admissible observations for loss aversion index in a well designed experiment.

Keywords: monotone class theorem; stochastic choice functional; embedded probability; comonotonic probability; isomorphism (search for similar items in EconPapers)
JEL-codes: C02 C44 D03 D81 (search for similar items in EconPapers)
Date: 2010-04-27
New Economics Papers: this item is included in nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/22380/1/MPRA_paper_22380.pdf original version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:22380

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().