Harin, Alexander (2015): An existence theorem for bounds (restrictions) on the expectation of a random variable. Its opportunities for utility and prospect theories.

PDF
MPRA_paper_66692.pdf Download (255kB)  Preview 
Abstract
An existence theorem is proved for the case of a discrete random variable with finite support. If the random variable takes on values in a finite interval and there is a lower nonzero bound on its dispersion, then nonzero bounds (or nonzero “forbidden zones”) on its expectation exist near the borders of the interval. The theorem can be used in utility and prospect theories, in particular, in the analysis of Prelec’s probability weighting function.
Item Type:  MPRA Paper 

Original Title:  An existence theorem for bounds (restrictions) on the expectation of a random variable. Its opportunities for utility and prospect theories 
Language:  English 
Keywords:  probability theory; dispersion; scatter; scattering; noise; economics; utility theory; prospect theory; decision theories; human behavior; Prelec; probability weighting function; 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General D  Microeconomics > D8  Information, Knowledge, and Uncertainty D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty 
Item ID:  66692 
Depositing User:  Alexander Harin 
Date Deposited:  16 Sep 2015 15:09 
Last Modified:  06 Oct 2019 04:22 
References:  Aczél, J., and R. D. Luce, “A behavioral condition for Prelec’s weighting function on the positive line without assuming W(1)=1,” Journal of Mathematical Psychology 51 (2007), pp. 126–129. Dokov, S. P., D.P. Morton. 2005. SecondOrder Lower Bounds on the Expectation of a Convex Function. Mathematics of Operations Research 30(3) 662–677 Harin, А., “The random–lottery incentive system. Can p~1 experiments deductions be correct?” 16th conference on the Foundations of Utility and Risk, 2014. Harin, А., (2012), “Data dispersion in economics (II) – Inevitability and Consequences of Restrictions”, Review of Economics & Finance 2 (2012), no. 4: 24–36. Kahneman, D., and R. Thaler, “Anomalies: Utility Maximization and Experienced Utility,” Journal of Economic Perspectives 20 (2006), no. 1, 221–234. Pinelis, I. 2011. Exact lower bounds on the exponential moments of truncated random variables. Journal of Applied Probability 48(2) 547560. Prékopa, A. 1990. The discrete moment problem and linear programming. Discrete Applied Mathematics 27(3) 235–254. Prékopa, A. 1992. Inequalities on Expectations Based on the Knowledge of Multivariate Moments. Lecture NotesMonograph Series 22 Stochastic Inequalities 309331. Schoemaker, P., and J. Hershey, “Utility measurement: Signal, noise, and bias,” Organizational Behavior and Human Decision Processes 52 (1992) no. 3, 397–424. Steingrimsson, R., and R. D. Luce, “Empirical evaluation of a model of global psychophysical judgments: IV. Forms for the weighting function,” Journal of Mathematical Psychology 51 (2007), pp. 29–44. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/66692 