Cadogan, Godfrey (2010): Asymptotic Theory Of Stochastic Choice Functionals For Prospects With Embedded Comotonic Probability Measures.

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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 comonotonic 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 BrouwerSchauder theory, guarantees fixed point convergence in convex choice sets. Along the way we introduce a risk operator in the HoffmanJorgensen class of lifting operators, and value function [averaging] operators with respect to Radon measure. In that set up, suitable binary operations on gainloss 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.
Item Type:  MPRA Paper 

Original Title:  Asymptotic Theory Of Stochastic Choice Functionals For Prospects With Embedded Comotonic Probability Measures 
Language:  English 
Keywords:  monotone class theorem; stochastic choice functional; embedded probability; comonotonic probability; isomorphism 
Subjects:  D  Microeconomics > D0  General > D03  Behavioral Economics; Underlying Principles D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C44  Operations Research; Statistical Decision Theory C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods 
Item ID:  22380 
Depositing User:  godfrey cadogan 
Date Deposited:  29. Apr 2010 00:38 
Last Modified:  11. Jan 2014 06:19 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/22380 