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Utility Theory
(Utility & Prospect & Decision Theories) (working papers mainly) See also Utility Theory metadata
Contents (in new windows)
1. Utility Theory News 2. Utility Theory Reviews & Analyses 3. Utility Theory Items Events ( December November October September August July June May April March February January 2010 Undated 2009 Undated 2008 Undated 2007 Undated ) 4. Utility Theory Past, Timeless Events 5. Utility Theory Problems (St. Petersburg Paradox Allais Paradox Equity Premium Puzzle Risk Aversion Gains and Losses Loss Aversion Overweighting of low Probabilities Underweighting of high Probabilities "Four-Fold-Pattern" Shape of Probability Weighting Function Ellsberg Paradox Preference Reversals ) 6. New Approach. Principle of Uncertain Future 7. Solution of Utility Theory Problems (of St. Petersburg Paradox of Allais Paradox of Equity Premium Puzzle of Risk Aversion of Gains and Losses of Loss Aversion of Overweighting of low Probabilities of Underweighting of high Probabilities of "Four-Fold-Pattern" of Shape of Probability Weighting Function of Ellsberg Paradox of Preference Reversals )
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1. Utility Theory News
Theorem of existence of ruptures for mean values on finite numerical segments. Discrete case Alexander Harin University Library of Munich, Germany Abstract Text Интервальный анализ распределений и разрывы Alexander Harin University Library of Munich, Germany Abstract Text Disentangling Motivational and Experiential Aspects of "Utility" - A Neuroeconomics Perspective Ulrich Witt and Martin Binder Max Planck Institute of Economics, Evolutionary Economics Group Abstract Text Book review: the tyranny of utility: behavioral social science and the rise of paternalism Arnaud Vaganay London School of Economics and Political Science Abstract Text Top
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2. Utility Theory Reviews & Analyses
Is There A Plausible Theory for Risky Decisions? James C. Cox, Vjollca Sadiraj, Bodo Vogt and Utteeyo Dasgupta Experimental Economics Center, Andrew Young School... 2007-06 Abstract Text Economists and uncertainty John Quiggin and Robert G. Chambers Risk and Sustainable Management Group, University ... 2005 Title Text Investigating Generalizations of Expected Utility Theory Using Experimental Data John Hey and Chris Orme Econometrica 1994 Abstract The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations Paul J H Schoemaker Journal of Economic Literature 1982 Title
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December
Theorem of existence of ruptures for mean values on finite numerical segments. Discrete case Alexander Harin University Library of Munich, Germany Abstract Text Интервальный анализ распределений и разрывы Alexander Harin University Library of Munich, Germany Abstract Text Stability of exponential utility maximization with respect to market perturbations Erhan Bayraktar and Ross Kravitz arXiv.org Abstract Text Shadow price in the power utility case Attila Herczegh and Vilmos Prokaj arXiv.org Abstract Text Disentangling Motivational and Experiential Aspects of "Utility" - A Neuroeconomics Perspective Ulrich Witt and Martin Binder Max Planck Institute of Economics, Evolutionary Economics Group Abstract Text Disappointment Models: an axiomatic approach Thierry Chauveau and Nicolas Nalpas HAL Abstract Text Top
November
Stochastic dominance with respect to a capacity and risk measures Miryana Grigorova HAL Abstract Text Book review: the tyranny of utility: behavioral social science and the rise of paternalism Arnaud Vaganay London School of Economics and Political Science Abstract Text Top
October
Forward-backward systems for expected utility maximization Ulrich Horst, Ying Hu, Peter Imkeller and Anthony Reveillac Humboldt University, Collaborative Research Center 649 Abstract Text Optimism and Pessimism with Expected Utility David Dillenberger, Andrew Postlewaite and Kareen Rozen Cowles Foundation for Research in Economics, Yale University Abstract Text Utility theory front to back - inferring utility from agents' choices Alexander M. G. Cox, David Hobson and Jan Obloj arXiv.org Abstract Text Top
September
An extension of the Becker proposition to non-expected utility theory Sanjit Dhami and Ali al-Nowaihi Department of Economics, University of Leicester Abstract Text Utility Maximization, Risk Aversion, and Stochastic Dominance Mathias Beiglboeck, Johannes Muhle-Karbe and Johannes Temme arXiv.org Abstract Text Stronger Utility Pavlo R. Blavatskyy Faculty of Economics and Statistics, University of Innsbruck Abstract Text On Admissible Strategies in Robust Utility Maximization Keita Owari arXiv.org Abstract Text Testing the Analytical Framework of Other-Regarding Preferences Vittiria Levati, Aaron Nicholas and Birendra Rai Monash University, Department of Economics Abstract Text Intertemporal substitution and recursive smooth ambiguity preferences Jianjun Miao and Takashi Hayashi Theoretical Economics Abstract Text The evolution of decision and experienced utility Arthur Robson and Larry Samuelson Theoretical Economics Abstract Text Top
August
Explaining the harmonic sequence paradox Ulrich Schmidt and Alexander Zimper Kiel Institute for the World Economy Abstract Text Ambiguous Volatility, Possibility and Utility in Continuous Time Larry Epstein and Shaolin Ji arXiv.org Abstract Text Additive habits with power utility: Estimates, asymptotics and equilibrium Roman Muraviev arXiv.org Abstract Text Risky Curves: From Unobservable Utility to Observable Opportunity Sets Daniel Friedman and Shyam Sunder Cowles Foundation for Research in Economics, Yale University Abstract Text Does Ambiguity Aversion Raise the Optimal Level of Effort? A Two-Period Model Loic Berger ULB -- Universite Libre de Bruxelles Abstract Text Smooth Ambiguity Aversion in the Small and in the Large Loic Berger ULB -- Universite Libre de Bruxelles Abstract Text The marginal utility of money: A modern Marshallian approach to consumer choice Jozsef Sakovics and Daniel Friedman (University of California at Santa Cruz) Edinburgh School of Economics, University of Edinburgh Abstract Text Non-monotonic utility functions for microeconomic analysis of sufficiency economy Komsan Suriya University Library of Munich, Germany Abstract Text Top
July
The Stability of the Constrained Utility Maximization Problem - A BSDE Approach Markus Mocha and Nicholas Westray arXiv.org Abstract Text BSDEs in Utility Maximization with BMO Market Price of Risk Christoph Frei, Markus Mocha and Nicholas Westray arXiv.org Abstract Text CRRA Utility Maximization under Risk Constraints Santiago Moreno-Bromberg, Traian A. Pirvu and Anthony Reveillac Humboldt University, Collaborative Research Center 649 Abstract Text A Step towards Valuing Utility the Marginal and Cardinal Way Paul Dolan, Daniel Fujiwara and Robert D Metcalfe Centre for Economic Performance, LSE Abstract Text Stability of exponential utility maximization with respect to market perturbations Erhan Bayraktar and Ross Kravitz arXiv.org Abstract Text On the utility representation of asymmetric single-peaked preferences Francisco Martinez Mora and M. Socorro Puy Department of Economics, University of Leicester Abstract Text June
On mental transformations Krzysztof Kontek University Library of Munich, Germany Abstract Text What is the actual shape of perception utility? Krzysztof Kontek University Library of Munich, Germany Abstract Text Equilibrium with exponential utility and non-negative consumption Roman Muraviev and Mario V. Wuethrich arXiv.org Abstract Text Power Utility Maximization in Discrete-Time and Continuous-Time Exponential Levy Models Johannes Temme arXiv.org Abstract Text Utility based pricing and hedging of jump diffusion processes with a view to applications Jochen Zahn arXiv.org Abstract Text Top
May
Subjective Risk, Confidence, and Ambiguity Christian P. Traeger Department of Agricultural & Resource Economics, UC Berkeley Abstract Text Transferable Utility Games with Uncertainty Helga Habis and P. Jean-Jacques Herings Institute of Economics, Hungarian Academy of Sciences Abstract Text The Bellman Equation for Power Utility Maximization with Semimartingales Marcel Nutz arXiv.org Abstract Text Top
April
Multivariate utility maximization with proportional transaction costs and random endowment Giuseppe Benedetti and Luciano Campi HAL Abstract Text Preference-Based Unawareness Burkhard Schipper University Library of Munich, Germany Abstract Text Discounting Models for Outcomes over Continuous Time Charles Harvey and Lars Peter Osterdal University of Copenhagen. Department of Economics Abstract Text Existence of Arrow-Debreu Equilibrium with Generalized Stochastic Differential Utility Patrick Bei?ner Bielefeld University, Institute of Mathematical Economics Abstract Text Utility Maximization, Risk Aversion, and Stochastic Dominance Mathias Beiglboeck, Johannes Muhle-Karbe and Johannes Temme arXiv.org Abstract Text Top
March
Portfolio optimization under model uncertainty and BSDE games Bernt Oksendal and Agnes Sulem HAL Abstract Text Utility theory front to back - inferring utility from agents' choices Alexander M. G. Cox, David Hobson and Jan Obloj arXiv.org Abstract Text On the Stability of Utility Maximization Problems Erhan Bayraktar and Ross Kravitz arXiv.org Abstract Text Ambiguous Volatility, Possibility and Utility in Continuous Time Larry Epstein and Shaolin Ji arXiv.org Abstract Text Top
February
Pessimism, Optimism and Credit Rationing Jean-Louis Leslie Arcand HAL Abstract Text Utility Indifference Pricing: A Time Consistent Approach Traian A Pirvu and Huayue Zhang arXiv.org Abstract Text Socio-economic utility and chemical potential Lemoy, R\'emi, Eric Bertin and Pablo Jensen arXiv.org Abstract Text Is utility transferable? A revealed preference analysis Laurens Cherchye, Thomas Demuynck and Bram De Rock Katholieke Universiteit Leuven, Centrum voor Economische Studien Abstract Text Top
January
Who Is (More) Rational? Syngjoo Choi, Shachar Kariv, Wieland Mueller and Dan Silverman Vienna Economics Papers Abstract Text Transitive regret Sushil Bikhchandani and Uzi Segal Theoretical Economics Abstract Text On the utility representation of asymmetric single-peaked preferences Francisco Martinez Mora and M. Socorro Puy Department of Economics, University of Leicester Abstract Text Duality in Robust Utility Maximization with Unbounded Claim via a Robust Extension of Rockafellar's Theorem Keita Owari arXiv.org Abstract Text Least Concave Ordinal Utility Function and The Marshallian Cardinal Utility Taradas Bandyopadhyay and Tapan Kumar Biswas Rimini Centre for Economic Analysis Abstract Text Top
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2010 Undated
Linking Decision and Time Utilities Krzysztof Kontek University Library of Munich, Germany Abstract Text Information, evolution and utility Larry Samuelson and Jeroen Swinkels David K. Levine Title Text Decision Utility Theory: Back to von Neumann, Morgenstern, and Markowitz Krzysztof Kontek University Library of Munich, Germany Abstract Text Were Jevons, Menger and Walras really cardinalists? On the notion of measurement in utility theory, psychology, mathematics and other disciplines, ca. 1870–1910 Ivan Moscati University of Turin Abstract Text Differences between Decision and Experienced Utility: An Investigation using the Choice Experiment method Sergio Colombo, Nick Hanley and Dugald Tinch University of Stirling, Division of Economics Abstract Text The Relative Utility Hypothesis With and Without Self-reported Reference Wages Adrian de la Garza, Giovanni Mastrobuoni, Atsushi Sannabe and Katsunori Yamada Institute of Social and Economic Research, Osaka University Abstract Text Horizon dependence of utility optimizers in incomplete models Kasper Larsen and Hang Yu arXiv.org Abstract Text Risk Preferences Are Not Time Preferences: Discounted Expected Utility with a Disproportionate Preference for Certainty James Andreoni and Charles Sprenger National Bureau of Economic Research, Inc Abstract Text The Price for Information about Probabilities and its Relation with Capacities Giuseppe Attanasi and Aldo Montesano University of Siena Abstract Text Eliciting Utility for (Non)Expected Utility Preferences Using Invariance Transformations Andre de Palma, Nathalie Picard and Jean-Luc Prigent HAL Abstract Text The evolution of decision and experienced utility Arthur Robson and Larry Samuelson Theoretical Economics Abstract Text A generalization of Rader's utility representation theorem Gianni Bosi and Magali Zuanon University Library of Munich, Germany Abstract Text Preference for Randomization: Ambiguity Aversion and Inequality Aversion Kaito Sato Northwestern University, Center for Mathematical Studies in Economics and Management Science Abstract Text Aggregating sets of von Neumann-Morgenstern utilities Eric Danan, Thibault Gajdos and Jean-Marc Tallon HAL Abstract Text Transitive regret Sushil Bikhchandani and Uzi Segal Theoretical Economics Abstract Text Classifying Behaviors in Risky Choices Krzysztof Kontek University Library of Munich, Germany Abstract Text Теорема о существовании разрывов в шкале вероятностей. Дискретный случай Alexander Harin University Library of Munich, Germany Abstract Text Theorem of existence of ruptures in probability scale. Preliminary short version Alexander Harin University Library of Munich, Germany Abstract Text Can the Consumption-Free Nonexpected Utility Model Solve the Risk Premium Puzzle? An Empirical Study of the Japanese Stock Market Myong-Il Kang Institute of Social and Economic Research, Osaka U... Abstract Text Horizon dependence of utility optimizers in incomplete models Kasper Larsen and Hang Yu arXiv.org Abstract Text Preference for Randomization: Ambiguity Aversion and Inequality Aversion Kaito Sato Northwestern University, Center for Mathematical S... Abstract Text A Salience Theory of Choice Errors Paola Manzini and Marco Mariotti Institute for the Study of Labor (IZA) Abstract Text Multi-Outcome Lotteries: Prospect Theory vs. Relative Utility Krzysztof Kontek University Library of Munich, Germany Abstract Text Теорема о существовании разрывов в шкале вероятностей. II Alexander Harin University Library of Munich, Germany Abstract Text Composite Prospect Theory: A proposal to combine ‘prospect theory’ and ‘cumulative prospect theory’ Ali al-Nowaihi and Sanjit Dhami Department of Economics, University of Leicester Abstract Text Stochastic Utilities With a Given Optimal Portfolio: Approach by Stochastic Flows N. El Karoui and M'Rad, Mohamed HAL Abstract Text Spectral Risk Measures: Properties and Limitations Kevin Dowd, John Cotter and Ghulam Sorwar Geary Institute, University College Dublin Abstract Text Stability of the utility maximization problem with random endowment in incomplete markets Constantinos Kardaras and Gordan Zitkovic arXiv.org Abstract Text Mean, Median or Mode? A Striking Conclusion From Lottery Experiments Krzysztof Kontek University Library of Munich, Germany Abstract Text Revealed Unawareness Burkhard Schipper University Library of Munich, Germany Abstract Text Теорема о существовании разрывов в шкале вероятностей Alexander Harin University Library of Munich, Germany Abstract Text Certain and Uncertain Utility: The Allais Paradox and Five Decision Theory Phenomena James Andreoni and Charles Sprenger David K. Levine Text Some aspects of random utility, extreme value theory and multinomial logit models Jonas Andersson and Jan Uboe Department of Finance and Management Science, Norw... Abstract Attitudes towards Uncertainty and Randomization: An Experimental Study Adam Dominiak and Wendelin Schnedler University of Heidelberg, Department of Economics Abstract Top
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2009 Undated
Ruptures in the probability scale? Calculation of ruptures’ dimensions Alexander Harin University Library of Munich, Germany Abstract Text The Illusion of Irrationality Krzysztof Kontek University Library of Munich, Germany Abstract Text Constructive Decision Theory Lawrence Blume, David Easley and Joseph Y. Halpern Institute for Advanced Studies Abstract Text Robust utility maximization for diffusion market model with misspecified coefficients R. Tevzadze and T. Toronjadze arXiv.org Abstract Text Transitive Regret Sushil Bikhchandani and Uzi Segal Boston College Department of Economics Abstract Text Are CEOs Expected Utility Maximizers? John List and Charles Mason National Bureau of Economic Research, Inc Abstract Text A Note on Utility Maximization with Unbounded Random Endowment Keita Owari Institute of Economic Research, Hitotsubashi Unive... Abstract Text Intergenerational justice when future worlds are uncertain Humberto Llavador, John E. Roemer and Joaquim Silvestre Department of Economics and Business, Universitat ... Abstract Text Absolute vs. Relative Notion of Wealth Changes Krzysztof Kontek University Library of Munich, Germany Abstract Text Utility, games, and narratives Guido Fioretti University Library of Munich, Germany Abstract Text General Equilibrium without Utility Functions: How far to go? Yves Balasko and Mich Tvede University of Copenhagen. Department of Economics Abstract Text Lottery valuation using the aspiration/relative utility function Krzysztof Kontek Department of Applied Econometrics, Warsaw School ... Abstract Text General correcting formula of forecasting? Alexander Harin MPRA Paper Abstract Text Общая корректирующая формула прогнозирования General forecasting correcting formula Alexander Harin MPRA Paper Abstract Text The Role of Role Uncertainty in Modified Dictator Games Nagore Iriberri and Pedro Rey-Biel Department of Economics and Business, Universitat ... Abstract Text A new solution to the Purchasing Power Parity puzzles: Risk-aversion, exchange rate uncertainty and the Law of One Price Michael Arghyrou, Andros Gregoriou and Panayiotis M. Pourpourides Cardiff University, Cardiff Business School, Econo... Abstract Text Choice deferral and ambiguity aversion Igor Kopylov Theoretical Economics Abstract Text Bounding the CRRA Utility Functions Richard M. H. Suen MPRA Paper Abstract Text Relating the two Dimensions of Risk Attitudes: An Experimental Analysis Jianying Qiu and Eva-Maria Steiger Friedrich-Schiller-University Jena, Max-Planck-Ins... Abstract Text Self Control, Risk Aversion, and the Allais Paradox Drew Fudenberg and David K Levine UCLA Department of Economics Title Text Top
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2008 Undated
Fuzzy interval net present value Marco Corazza and Silvio Giove Department of Applied Mathematics, University of V... Abstract Text Realization Utility Nicholas C. Barberis and Wei Xiong National Bureau of Economic Research, Inc Abstract Text Subjective expected utility in games Alfredo Di Tillio Theoretical Economics Abstract Text Consistency and the core for fuzzy non-transferable-utility games Yu-Hsien Liao Economics Bulletin Abstract Text Comparison of Mean-Variance Theory and Expected-Utility Theory through a Laboratory Experiment Andrea Morone Economics Bulletin Abstract Text A general theory of time discounting: The reference-time theory of intertemporal choice Ali al-Nowaihi and Sanjit Dhami Department of Economics, University of Leicester Abstract Text Strotz meets Allais: Diminishing Impatience and the Certainty Effect Yoram Halevy Microeconomics.ca Website Title Text Ellsberg Revisited: an Experimental Study Yoram Halevy Microeconomics.ca Website Title Text Manipulating Reference States: the Effect of Attitudes on Utility Astrid Matthey Friedrich-Schiller-University Jena, Max-Planck-Ins... Title Text Calibration Results for Non-Expected Utility Theories Zvi Safra and Uzi Segal Boston College Department of Economics Title Text Facts, Norms and Expected Utility Functions Sophie Jallais, Pradier, Pierre-Charles and David Teira HAL Title Text Solution of the Ellsberg paradox by means of the principle of uncertain future Alexander Harin University Library of Munich, Germany Title Text The Descriptive and Predictive Adequacy of Theories of Decision Making Under Uncertainty/Ambiguity John Hey, Gianna Lotito and Anna Maffioletti Department of Economics, University of York Title Text Non Utility Maximizing Behaviour: Probabilistic Choice in a Budget Set “Box”. Properties of Expected Demand Functions Larsson, Lars-Goran Goteborg University, Department of Economics Title Text Towards a Characterization of Rational Expectations Itai Arieli UCLA Department of Economics Title Text Utility-Based Utility David Cass Penn Institute for Economic Research, Department o... Abstract Text Parametric Weighting Functions Enrico Diecidue, Ulrich Schmidt and Horst Zank Kiel Institute for the World Economy Abstract Text Top
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2007 Undated
Testing Guilt Aversion Tore Ellingsen, Magnus Johannesson, Sigve Tjotta and Gaute Torsvik Stockholm School of Economics Abstract Text SHOULD THE UTILITY FUNCTION BE DITCHED? Dominique, C-Rene University Library of Munich, Germany Abstract Text Share the Gain, Share the Pain? Almost Transferable Utility, Changes in Production Possibilities, and Bargaining Solutions Elisabeth Gugl Department of Economics, University of Victoria Abstract Text Non-Monotonicity of the Tversky-Kahneman Probability-Weighting Function: a Cautionary Note JONATHAN E. INGERSOLL JR. Jr. Yale School of Management, International Center for Finance Abstract+Text On Behavioral Complementarity and its Implications Christopher P. Chambers, Federico Echenique and Eran Shmaya Documentos de Trabajo (working papers) Abstract Text Принцип неопределенного будущего и его применения А. Харин СОЦИОНЕТ About: A Solution of the Ellsberg Paradox by means of the Principle of Uncertain Future. Аннотация Текст Probabilities in Economic Modeling Itzhak Gilboa, Andrew Postlewaite and David Schmeidler UCLA Department of Economics Title Text Exponential Spectral Risk Measures Kevin Dowd and John Cotter Working Paper Series Abstract + Text Rationality on the Rise: Why Relative Risk Aversion Increases with Stake Size Fehr-Duda, Helga, Adrian Bruhin, Thomas F. Epper and Renate Schubert University of Zurich, Socioeconomic Institute Abstract Text Is There A Plausible Theory for Risky Decisions? James C. Cox, Vjollca Sadiraj, Bodo Vogt and Utteeyo Dasgupta Experimental Economics Center, Andrew Young School... Abstract Text Statistics of Risk Aversion Enzo Giacomini and Wolfgang Karl H?rdle Humboldt University, Collaborative Research Center... Abstract Text Why Kill Politicians? A Rational Choice Analysis of Political Assassinations Bruno S. Frey Center for Research in Economics, Management and t... Abstract Text Mixture Models of Choice Under Risk Anna Conte, John Hey and Peter Grant Moffatt Department of Economics, University of York Abstract Text Delay aversion Efe A. Ok and Benoit, Jean-Pierre Theoretical Economics Abstract Text Should National Happiness be Maximized? Bruno S. Frey and Alois Stutzer Center for Research in Economics, Management and t... Abstract Text An economic index of riskiness Robert J. Aumann and Roberto Serrano Instituto Madrile?o de Estudios Avanzados (IMDEA) ... Abstract Text Principle of uncertain future and utility Alexander Harin University Library of Munich, Germany Abstract Text Noise and Bias in Eliciting Preferences John Hey, Andrea Morone and Ulrich Schmidt Department of Economics, University of York Abstract Text Top
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Utility Theory
Events 4. Past, Timeless Anomalies: Utility Maximization and Experienced Utility Daniel Kahneman and Richard H. Thaler Journal of Economic Perspectives 2006 Abstract Text of the corresponding Working Paper Prospect Theory: An Analysis of Decision under Risk Daniel Kahneman and Amos Tversky Econometrica 1979 Title Risk, Ambiguity, and the Savage Axioms Daniel Ellsberg The Quarterly Journal of Economics 1961 Abstract Le comportement de l'homme rationnel devant le risque: critique des postulats et axiomes de l'Ecole Americaine Maurice Allais Econometrica 1953 Title Theory of Games and Economic Behavior John von Neumann and Oskar Morgenstern Princeton University Press 1944 Table of contents Text (txt 1.6 MB) Text (pdf 33 MB) An Introduction to the Principles of Morals and Legislation Jeremy Bentham The Online Library of Liberty 1823 Contents Text Exposition of a New Theory on the Measurement of Risk Daniel Bernoulli Commentarii Academiae Scientiarum Imperialis Petropolitanae 1738 Title Top
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5. Utility Theory Problems & Paradoxes
(more)
The Allais paradox (modified)
Suppose Mr. Somebody offers you a choice of only one of the following: A guaranteed gain of $99. Or A lottery: The gain of $100 with the probability P(preliminary) = 99% or $0 with the (preliminary) probability 1%. The mathematical expectations of guarantee and lottery outcomes are exactly the same. But people chose the guaranteed gain instead of the lottery. Top
Gains and Losses
Compare two experiments: 1) Mr. Somebody offers you a choice of only one of the following: A guaranteed gain of $99. Or A lottery: The gain of $100 with the probability P(preliminary) = 99% or $0 with the (preliminary) probability 1%. 2) Mr. Somebody offers you a choice of only one of the following: A guaranteed loss of $99. Or A lottery: The loss of $100 with the probability P(preliminary) = 99% or $0 with the (preliminary) probability 1%. The mathematical expectations of the guarantee and lottery outcomes are exactly the same in both experiments. But in similar experiments, the overwhelming majority of people chose: - in the case of gains - the guaranteed gain instead of the lottery one. - in the case of losses - the lottery loss instead of the guaranteed one. The possible well-known "natural and clear explanation" of gains in the Allais paradox by means of risk aversion cannot supply any uniform explanation for both gains and losses. The result of this explanation is gains' risk aversion and losses' risk seeking. Top
Overweighting of low Probabilities
Suppose Mr. Somebody offers you a choice of only one of the following: A guaranteed gain of $1. Or A lottery: The gain of $100 with the probability P(preliminary) = 1% or $0 with the (preliminary) probability 1%. The mathematical expectations of guarantee and lottery outcomes are exactly the same. But the well-determined experimental fact is: in similar experiments the obvious majority of people chose the lottery instead of the guaranteed gain.
Four-Fold-Pattern
The well-determined facts are: For positive (gains) risky prospects, people typically 1) overweight low probabilities but 2) underweight high probabilities. For negative (losses) risky prospects, people typically 3) underweight low probabilities but 4) overweight high probabilities. Top
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6. New Approach
(more)
The idea of the approach
Particular consideration of (hidden) uncertainties (noises, fluctuations, measurements' errors, imprecision, etc.)
Principle of Uncertain Future
(simplified as much as possible)
The principle
The probability of a future event contains uncertainty.
6.1. The first consequence of the principle
Suppose we plan to test the probability value, which is equal to 99%. Suppose the probability uncertainty value is equal to 5%. Then, evidently, the real mean value of probability cannot be as high as 99%. Generally, High probabilities will decrease.
Phigh real < Phigh planned
Analogously, but considering the second consequence of the principle (see below),
Low probabilities can increase.
Plow real possible > Plow planned
6.2. The second consequence of the principle
The total probability of unforeseen future events is more than 0%
Σ Punforeseen real > 0%
Hence,
The present total probability of future events is less than 100%
Σ Pplanned < 100%
or
The present probability system of future events is incomplete. Top
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7. Solution of Utility Theory Problems
(more)
The strongest qualitative test is the 4-Fold-Pattern.
Solution & Explanation
of the Four-Fold-Pattern (simplified as much as possible) The well-determined facts are: For positive (gains) risky prospects, people typically 1) overweight low probabilities but 2) underweight high probabilities. For negative (losses) risky prospects, people typically 3) underweight low probabilities but 4) overweight high probabilities. Denoting the real value of probability, which value is near 100% as Phigh real , the (positive) value of gain as G and the (negative) value of loss as -G , we obtain
Phigh real < Phigh planned
and
G * Phigh real < G * Phigh planned
-G * Phigh real > -G * Phigh planned
2) the underweight of high probabilities gains and 4) the overweight of high probabilities losses. Denoting the real value of probability, which value is near 0% as Plow real possible we obtain
Plow real possible > Plow planned
and
G * Plow real possible > G * Plow planned
-G * Plow real possible < -G * Plow planned
1) the overweight of low probabilities gains and 3) the underweight of low probabilities losses. Thus, the above facts can be explained naturally and uniformly. Top
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