The Need for Discontinuous Probability Weighting Functions: How Cumulative Prospect Theory is torn between the Allais Paradox and the St. Petersburg Paradox

2019 ◽  
Author(s):  
Maik Dierkes ◽  
Vulnet Sejdiu
Keyword(s):  
Prospect Theory ◽  
Cumulative Prospect Theory ◽  
Probability Weighting ◽  
Allais Paradox ◽  
Weighting Functions ◽  
Petersburg Paradox

scholarly journals Cumulative prospect theory and the St. Petersburg paradox

2006 ◽  
Vol 28 (3) ◽  
pp. 665-679 ◽  
Author(s):  
Marc Oliver Rieger ◽  
Mei Wang
Keyword(s):  
Prospect Theory ◽  
Cumulative Prospect Theory ◽  
Petersburg Paradox

scholarly journals Dynamic prospect theory - two core economic decision theories coexist in the gambling behavior of monkeys

2021 ◽  
Author(s):  
Agnieszka Tymula ◽  
Yuri Imaizumi ◽  
Takashi Kawai ◽  
Jun Kunimatsu ◽  
Masayuki Matsumoto ◽  
...  
Keyword(s):  
Reinforcement Learning ◽  
Prospect Theory ◽  
Weighting Function ◽  
Gambling Behavior ◽  
Theory Model ◽  
Probability Weighting ◽  
Choice Data ◽  
Mathematical Functions ◽  
Weighting Functions ◽  
Dynamic Function

Research in behavioral economics and reinforcement learning has given rise to two influential theories describing human economic choice under uncertainty. The first, prospect theory, assumes that decision-makers use static mathematical functions, utility and probability weighting, to calculate the values of alternatives. The second, reinforcement learning theory, posits that dynamic mathematical functions update the values of alternatives based on experience through reward prediction error (RPE). To date, these theories have been examined in isolation without reference to one another. Therefore, it remains unclear whether RPE affects a decision-maker's utility and/or probability weighting functions, or whether these functions are indeed static as in prospect theory. Here, we propose a dynamic prospect theory model that combines prospect theory and RPE, and test this combined model using choice data on gambling behavior of captive macaques. We found that under standard prospect theory, monkeys, like humans, had a concave utility function. Unlike humans, monkeys exhibited a concave, rather than inverse-S shaped, probability weighting function. Our dynamic prospect theory model revealed that probability distortions, not the utility of rewards, solely and systematically varied with RPE: after a positive RPE, the estimated probability weighting functions became more concave, suggesting more optimistic belief about receiving rewards and over-weighted subjective probabilities at all probability levels. Thus, the probability perceptions in laboratory monkeys are not static even after extensive training, and are governed by a dynamic function well captured by the algorithmic feature of reinforcement learning. This novel evidence supports combining these two major theories to capture choice behavior under uncertainty.

Cumulative Prospect Theory, Option Returns, and the Variance Premium

2018 ◽  
Vol 32 (9) ◽  
pp. 3667-3723 ◽  
Author(s):  
Lieven Baele ◽  
Joost Driessen ◽  
Sebastian Ebert ◽  
Juan M Londono ◽  
Oliver G Spalt
Keyword(s):  
Prospect Theory ◽  
Cumulative Prospect Theory ◽  
Probability Weighting ◽  
Asset Pricing Model ◽  
Equilibrium Asset Pricing ◽  
Option Returns ◽  
Dynamic Setting ◽  
Editorial Decision ◽  
Equity Index ◽  
Index Option

Abstract We develop a tractable equilibrium asset pricing model with cumulative prospect theory (CPT) preferences. Using GMM on a sample of U.S. equity index option returns, we show that by introducing a single common probability weighting parameter for both tails of the return distribution, the CPT model can simultaneously generate the otherwise puzzlingly low returns on both out-of-the-money put and out-of-the-money call options as well as the high observed variance premium. In a dynamic setting, probability weighting and time-varying equity return volatility combine to match the observed time-series pattern of the variance premium. Received May 30, 2017; editorial decision August 10, 2018 by Editor Andrew Karolyi.

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)

scholarly journals Asymmetrical Property of the Subproportionality of Weighting Function in Prospect Theory: Is It Real and How Can It Be Achieved?

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1928
Author(s):  
Yuan-Na Huang ◽  
Si-Chu Shen ◽  
Shu-Wen Yang ◽  
Yi Kuang ◽  
Yun-Xiao Li ◽  
...  
Keyword(s):  
Prospect Theory ◽  
Weighting Function ◽  
Underlying Mechanism ◽  
Risky Choice ◽  
High Impact ◽  
Current Understanding ◽  
Probability Weighting ◽  
Allais Paradox ◽  
Probability Weighting Function ◽  
Decision Mechanisms

An asymmetrical property of the probability weighting function, namely, subproportionality, was derived from observations. Subproportionality can provide a reasonable explanation for accommodating the Allais paradox and, therefore, deserves replication for its high impact. The present study aimed to explore the mechanism of subproportionality by comparing the two completely opposite decision mechanisms: prospect theory and equate-to-differentiate theory. Results revealed that the underlying mechanism supports the prediction of equate-to-differentiate theory but not prospect theory in the diagnostic stimuli condition. Knowledge regarding which intra-dimensional difference between Options A and B is greater, not knowledge regarding which option’s overall prospect value is greater, indeed predicts option preference. Our findings may deepen current understanding on the mechanisms behind the simple risky choice with a single-non-zero outcome. Additionally, these findings will hopefully encourage subsequent researchers to take a fresh look at the Allais paradox.

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