A Probability Weighting Function for Cumulative Prospect Theory and Mean-Gini Approach to Optimal Portfolio Investment

2013 ◽  
Author(s):  
Pavlo R. Blavatskyy
Keyword(s):  
Prospect Theory ◽  
Weighting Function ◽  
Cumulative Prospect Theory ◽  
Optimal Portfolio ◽  
Portfolio Investment ◽  
Probability Weighting ◽  
Probability Weighting Function

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.

scholarly journals On the Empirical Validity of Cumulative Prospect Theory: Experimental Evidence of Rank‐Independent Probability Weighting

Econometrica ◽  
2020 ◽  
Vol 88 (4) ◽  
pp. 1363-1409
Author(s):  
B. Douglas Bernheim ◽  
Charles Sprenger
Keyword(s):  
Experimental Evidence ◽  
Prospect Theory ◽  
Weighting Function ◽  
Cumulative Prospect Theory ◽  
Probability Weighting ◽  
Nonparametric Method ◽  
Relative Probability ◽  
Order Of Magnitude ◽  
Probability Weight ◽  
Independent Probability

Cumulative Prospect Theory (CPT), the leading behavioral account of decisionmaking under uncertainty, avoids the dominance violations implicit in Prospect Theory (PT) by assuming that the probability weight applied to a given outcome depends on its ranking. We devise a simple and direct nonparametric method for measuring the change in relative probability weights resulting from a change in payoff ranks. We find no evidence that these weights are even modestly sensitive to ranks. Conventional calibrations of CPT preferences imply that the percentage change in probability weights should be an order of magnitude larger than we observe. It follows either that probability weighting is not rank‐dependent, or that the weighting function is nearly linear. Nonparametric measurement of the change in relative probability weights resulting from changes in probabilities rules out the second possibility. Additional tests nevertheless indicate that the dominance patterns predicted by PT do not arise. We reconcile these findings by positing a form of complexity aversion that generalizes the well‐known certainty effect.

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.

Video conferencing software selection based on hybrid MCDM and cumulative prospect theory under a major epidemic

2021 ◽  
pp. 1-18
Author(s):  
Jie Xu ◽  
Jian Lv ◽  
Hong-Tai Yang ◽  
Yan-Lai Li
Keyword(s):  
Prospect Theory ◽  
Weighting Function ◽  
Video Conferencing ◽  
Cumulative Prospect Theory ◽  
Reference Points ◽  
Software Selection ◽  
Interval Numbers ◽  
The Matrix ◽  
Selection Decision ◽  
Gains And Losses

The video conferencing software is regarded as a significant tool for social distancing and getting incorporations up and going. Due to the indeterminacy of epidemic evolution and the multiple criteria, this paper proposes a video conferencing software selection method based on hybrid multi-criteria decision making (HMCDM) under risk and cumulative prospect theory (CPT), in which the criteria values are expressed in various mathematical forms (e.g., real numbers, interval numbers, and linguistic terms) and can be changed with natural states of the epidemic. Initially, the detailed description of video conferencing software selection problem under an epidemic are given. Subsequently, a whole procedure for video conferencing software selection is conducted, the approaches for processing and normalizing the multi-format evaluation values are presented. Furthermore, the expectations provided by DMs under different natural states of the epidemic are considered as the corresponding reference points (RP). Based on this, the matrix of gains and losses is constructed. Then, the prospect values of all criteria and the perceived probabilities of natural states are calculated according to the value function and the weighting function in CPT respectively. Finally, the proposed method is illustrated by an empirical case study, and the comparison analysis and the sensitivity analysis for the loss aversion parameter are conducted to prove the effectiveness and robustness. The results show that considering the psychological characteristics of DMs in selection decision is beneficial to avoid the unacceptable and potential loss risks. This study could provide a useful guideline for managers who intend to select appropriate video conferencing software.

A cognitive-emotional account of the shape of the probability weighting function

2002 ◽  
Vol 15 (2) ◽  
pp. 79-100 ◽  
Author(s):  
Eduard Brandstätter ◽  
Anton Kühberger ◽  
Friedrich Schneider
Keyword(s):  
Weighting Function ◽  
Probability Weighting ◽  
Probability Weighting Function
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