Estimation and Comparison Between Rank-Dependent Expected Utility, Cumulative Prospect Theory and Quantum Decision Theory

2020 ◽  
Author(s):  
Giuseppe Ferro ◽  
Tatyana Kovalenko ◽  
Didier Sornette
Keyword(s):  
Decision Theory ◽  
Prospect Theory ◽  
Expected Utility ◽  
Cumulative Prospect Theory ◽  
Quantum Decision Theory ◽  
Rank Dependent Expected Utility

scholarly journals Cumulative Prospect Theory Version with Fuzzy Values of Outcome Estimates

Risks ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 72
Author(s):  
Oleg Uzhga-Rebrov ◽  
Peter Grabusts
Keyword(s):  
Prospect Theory ◽  
Expected Utility ◽  
Utility Theory ◽  
Expected Utility Theory ◽  
Cumulative Prospect Theory ◽  
Development History ◽  
Decisions Under Risk ◽  
History Of ◽  
Main Factors ◽  
Theoretical Foundations

Choosing solutions under risk and uncertainty requires the consideration of several factors. One of the main factors in choosing a solution is modeling the decision maker’s attitude to risk. The expected utility theory was the first approach that allowed to correctly model various nuances of the attitude to risk. Further research in this area has led to the emergence of even more effective approaches to solving this problem. Currently, the most developed theory of choice with respect to decisions under risk conditions is the cumulative prospect theory. This paper presents the development history of various extensions of the original expected utility theory, and the analysis of the main properties of the cumulative prospect theory. The main result of this work is a fuzzy version of the prospect theory, which allows handling fuzzy values of the decisions (prospects). The paper presents the theoretical foundations of the proposed version, an illustrative practical example, and conclusions based on the results obtained.

BETTING MARKET: Rank Dependent Expected Utility

2013 ◽  
Vol 1 (2) ◽  
pp. 147-163
Author(s):  
Loreto Llorente
Keyword(s):  
Decision Theory ◽  
Expected Utility ◽  
Utility Maximization ◽  
Betting Market ◽  
Expected Utility Maximization ◽  
Classical Decision ◽  
Rank Dependent Expected Utility ◽  
The Way

In Pelota matches, games with two mutually exclusive and exhaustive outcomes, bets on the winner are made through a middleman who receives 16% of the finally paid amount. The classical decision theory of expected utility maximization can not explain this market assuming bettors are identical. Llorente and Aizpurua (2007) explain the existence of bets in the market under Quiggin’s rank dependent expected utility (RDEU) model. They find that bettors have to be optimistic in order to explain the existence of a bet. Analyzing the way odds are fixed in the market Llorente (2006) finds that assuming equal return on bets there are inefficiencies in the market. In this paper we show that, given an assumption that bettors are rank dependent expected utility maximizers, these inefficiencies tend to disappear.

Subjective Skewness of Return as an Explanation of the Optimal Choice between Gambles in Cumulative Prospect Theory

2013 ◽  
Vol 2 (2) ◽  
pp. 97-108
Author(s):  
David Peel
Keyword(s):  
Utility Function ◽  
Prospect Theory ◽  
Expected Utility ◽  
Cumulative Prospect Theory ◽  
Optimal Choice ◽  
Decision Makers ◽  
Expected Return ◽  
Positive Skewness

Given that the expected return and variance of return of two gambles are equal  the hypothesis that the gamble with the greater  positive skewness of return will be chosen by an expected utility maximiser is appealing. However the hypothesis is  not, in general, correct. Brockett and Garven (1998) and Brocket and Kahane (1992) demonstrate this both theoretically and by constructing counter examples.A particularly revealing example is the following one constructed by Brockett and Kahane.  Gamble A has the two outcomes 2.45 and 7.49 with probabilities 0.5141 and 0.4859 respectively. Gamble B has the three outcomes 0, 4.947 and 10 with probabilities 0.12096, 0.750085 and 0.128955 respectively. Even though gamble A exhibits  lower expected return,  a higher variance and lower  positive skewness than gamble B it is preferred to gamble B by an expected utility maximiser on the basis of any standard utility function  such as power, log or exponential.  Consequently in this  example of theirs the expected utility maximiser exhibits an aversion to higher expected return and higher skewness and a preference for higher variance. As noted by Brockett and Kahane these results cannot be dismissed as decision makers “trading” variance for mean or skewness or having a strange idiosyncratic utility function.

scholarly journals Stocks as Lotteries: The Implications of Probability Weighting for Security Prices

2008 ◽  
Vol 98 (5) ◽  
pp. 2066-2100 ◽  
Author(s):  
Nicholas Barberis ◽  
Ming Huang
Keyword(s):  
Asset Pricing ◽  
Prospect Theory ◽  
Expected Utility ◽  
Cumulative Prospect Theory ◽  
Excess Return ◽  
Probability Weighting ◽  
Utility Model ◽  
Security Prices ◽  
Global Optima ◽  
Expected Utility Model

We study the asset pricing implications of Tversky and Kahneman's (1992) cumulative prospect theory, with a particular focus on its probability weighting component. Our main result, derived from a novel equilibrium with nonunique global optima, is that, in contrast to the prediction of a standard expected utility model, a security's own skewness can be priced: a positively skewed security can be “overpriced” and can earn a negative average excess return. We argue that our analysis offers a unifying way of thinking about a number of seemingly unrelated financial phenomena. (JEL D81, G11, G12)

Probability Dominance

2020 ◽  
Vol 102 (5) ◽  
pp. 1006-1020
Author(s):  
Enrico Diecidue ◽  
Haim Levy ◽  
Moshe Levy
Keyword(s):  
Decision Making ◽  
Prospect Theory ◽  
Expected Utility ◽  
Cumulative Prospect Theory ◽  
Economic Consequences ◽  
Regret Theory ◽  
Decisions Under Risk ◽  
Set Up ◽  
Winner Take All ◽  
Probability Dominance

The most commonly employed paradigms for decision making under risk are expected utility, prospect theory, and regret theory. We examine the simple heuristic of maximizing the probability of being ahead, which in some natural economic situations may be in contradiction to all three of the above fundamental paradigms. We test whether this heuristic, which we call probability dominance (PD), affects decisions under risk. We set up head-to-head situations where all preferences of a given class (expected utility, original or cumulative prospect theory, or regret theory) favor one alternative yet PD favors the other. Our experiments reveal that 49% of subjects' choices are aligned with PD in contradiction to any form of expected utility or prospect theory maximization; 73% are aligned with PD as opposed to preferences under risk aversion and under original and cumulative prospect theory preferences; and 68% to 76% are aligned with PD contradicting preferences under regret theory. We conclude that probability dominance substantially affects choices and should therefore be incorporated into decision-making models. We show that PD has significant economic consequences. The PD heuristic may have evolved through situations of winner-take-all competition.

scholarly journals Law & Economics as a Theory of Decision Making in Legal Contexts – Decision Theoretical Foundations, Their Misinterpretations and Excessive Claims of Economic Analysis of Law

2012 ◽  
pp. 34-50
Author(s):  
Magdalena Małecka
Keyword(s):  
Decision Making ◽  
Economic Analysis ◽  
Decision Theory ◽  
Prospect Theory ◽  
Expected Utility ◽  
Economic Analysis Of Law ◽  
Legal Norms ◽  
Legal Contexts ◽  
Theoretical Foundations ◽  
The Way

The article treats law & economics as a proposal of a theory of decision making in legal settings. It is emphasized that the distinction between two approaches in economic analysis of law: the neoclassical and the behavioral one, is made with reference to two different theories of decision making applied in the realm of each approach. The neoclassical approach is based on the theory of expected utility, whereas the behavioral one – on prospect theory. According to the scholars on both sides, application of decision theory might be helpful in influencing behavior by legal norms in a more sophisticated way. The claim of the article is that law & economics scholars misinterpret the assumptions and propositions of the theories and/or formulate excessive claims, if they argue that decision theoretical findings provide knowledge about the way in which people’s decisions are influenced by law.

scholarly journals From expected utility theory to prospect theory: tracking down the experimental path after forty years

2020 ◽  
Vol 30 (4) ◽  
Author(s):  
Sławomir Kalinowski
Keyword(s):  
Experimental Study ◽  
Prospect Theory ◽  
Expected Utility ◽  
Research Program ◽  
Utility Theory ◽  
Scientific Research ◽  
Expected Utility Theory ◽  
Cumulative Prospect Theory ◽  
The Other ◽  
Scientific Research Program

The article is an experimental study testing the expected utility theory axioms. Three of the experiments are a repetition of a previous test, while the other two are original. The repeated experiments were performed in slightly changed circumstances. The participants were incentivised with rewards, which did not happen in the tree replicated tests. The results confirmed degeneration of the expected utility theory as a scientific research program. The evidence that emerged from the tests supported the hypothesis on the cumulative prospect theory predicting facts not forecasted by the EUT.

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