Value Function Of Prospect Theory Research Articles

PDHL-MARCOS method based on cumulative prospect theory for MAGDM and its application in network security evaluation

The increasingly large and complex network brings convenience to our life and production, but it also brings potential dangers. Any minor vulnerability may lead to failure of application software configuration, software maintenance, user management and system management. Eventually, our network is interrupted, and even life and production data are leaked. Therefore, establishing a scientific and effective network security evaluation model is an effective way to supervise, manage and improve network security; It is also an effective measure to reduce the loss of life and production. Therefore, we first selected six factors closely related to network security to form a complete network security evaluation index system. Then, the utility function in the traditional measurement of alternatives and ranking according to compromise solution (MARCOS) method is improved by using the value function in cumulative prospect theory (CPT), and a PDHL-MARCOS evaluation model that can reflect the decision-makers’ (DMs’) attitudes towards gains and losses is obtained in the probabilistic double hierarchy linguistic term set (PDHLTS). In addition, the relative entropy (RE) method is also used to obtain expert weights. The combination weights of attributes are obtained using the correlation coefficient and the standard deviation (CCSD) method and the weight function in CPT.

Requirement-driven sustainable supplier selection: Creating an integrated perspective with stakeholders' interests and the wisdom of expert crowds

Driven by the pressure from various stakeholders to embrace sustainability and from the market to enhance competitiveness, more and more companies have been committed to conducting sustainable supplier selection (SSS). SSS is a requirement-driven multi-criteria decision-making (MCDM) problem and the existing literatures have attempted to integrate quality function deployment (QFD) with various MCDM methods to model the problem. However, these models have not conducted SSS based on stakeholders’ satisfaction from alternatives, and used the weights of criteria obtained from stakeholders’ preferences for requirements, which is used to model the compensation among satisfaction levels of different requirements, to guide the compensation among alternatives’ performances on different criteria. In order to address these deficiencies, this paper develops a novel generalized (QFD)-based MCDM structure for SSS, based on which we further design a QFD-based multi-stakeholders and multi-experts MCDM model considering stakeholders’ consensus of interest and wisdom of expert crowds. Firstly, multiple stakeholder groups with multiple participants in each one are asked to output their expectations and preferences for their own requirements; within each group, the algorithm for consensus reaching process (CRP) is designed to formulate the acceptable collective expectations, and the best worst method (BWM) method integrated with an algorithm for consistency improving process (CIP) and an algorithm for CRP is developed to weight requirements. Secondly, multiple experts use basic uncertain linguistic information (BULI) to characterize performances of alternatives on criteria and relationship between requirements and criteria, and a method of weighting individual judgements with the capability of drawing on wisdom of crowds (WOC) while accommodating organizers’ trust level in reliability given by experts is used to facilitate formulating collective judgements. Thirdly, for each alternative and each requirement of each stakeholder group, we can quantify the comprehensive performance of the alternative on the requirement with the help of QFD, based on which and the group’s expectation we can use the value function of prospect theory to quantify the group’s satisfaction of the requirement from the alternative; aggregating the weighted satisfaction levels of requirements gives rise to the comprehensive satisfaction level of each group from each alternative; and then the Maximin decision rule is introduced to rank alternatives because of its ability of accommodating the non-compensation among different stakeholder groups. Finally, a case study is conducted to investigate the validity and effectiveness of the proposed model.

Research on travel path choice considering complex environment: theory, model and case

In this paper, considering the heterogeneity of travelers’ decision-making behavior caused by travel environment factors, thus affecting the choice of travel path, the theories and methods of travel path choice based on improved cumulative prospect theory (ICPT) in complex environment were proposed. On the basis of cumulative prospect theory (CPT), the value function was improved, and the parameter value range was enlarged. The nonlinear curve of value function and weight function of cumulative prospect theory was fitted through thousands of data tests and experiments. Then according to the decision preference, the decision makers were divided into different categories and the reference point value relationship of heterogeneous decision makers was found. In this paper, fuzzy travel time reference point and periodic dynamic risk degree reference point were set up, and a dynamic path selection model based on heterogeneous double reference point was established to improve the cumulative prospect value. Taking the highway network in Sichuan-Tibet region for example, the optimal path selection scheme of heterogeneous travel groups under the complex environmental factors such as debris flow and landslide in each time stage was studied, and the influence of preference parameter of travel time and risk degree on path choice was analyzed, and then the parameter sensitivity in the cumulative prospect theory (ICPT) was analyzed. The research results verified the rationality of the improved theory and method proposed in this study, which not only provide a new way of thinking for the study of travel path choice in complex environment but also provide theoretical guidance value for supporting regional traffic planning and construction in complex environment.

Rapidly diminishing sensitivity and discrete sensitivity: Explaining people's sensitivity to outcomes across decisions.

Classic theories of perception, cognition, judgment, and decision making assert that people exhibit diminishing sensitivity to magnitude changes. For instance, according to the value function of prospect theory (Kahneman & Tversky, 1979), the pleasure of moving from 0 to $1000 is larger than the pleasure of moving from $1000 to $2000, whereas the pleasure of moving from $1000 to $2000 is larger than the pleasure of moving from $2000 to $3000. In this article, I call into question how much diminishing sensitivity actually impacts choice and the nature of the value function. I advance a special form of diminishing sensitivity that I have termed rapidly diminishing sensitivity, which postulates that people are sensitive to the presence versus the absence of outcomes but are less sensitive to the scope of the outcomes when the latter differ from zero. Rapidly diminishing sensitivity yields a value function that flattens out rapidly as values move away from zero. In the special case where the value function flattens out immediately after zero, rapidly diminishing sensitivity assumes a discrete form that I have termed discrete sensitivity. I propose that rapidly diminishing sensitivity and discrete sensitivity are typically observed in experimental studies that involve extensive manipulations of the size of the outcomes across decisions, holding everything else constant. I provide evidence for my hypothesis in eight well-powered preregistered experiments across a wide range of domains, such as financial decisions, valuations of human lives, purchase decisions, judgments of goal-related performance, intertemporal choices, and moral decisions. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

The Effect of Relative Income Concerns on Life Satisfaction: Relative Deprivation and Loss Aversion

Income comparisons are important for individual well-being. We examine the shape of the relationship between relative income and life satisfaction, and test empirically if the features of the value function of prospect theory carry over to experienced utility. We draw on a unique panel dataset for a middle-income country that allows us to work with an endogenous reference income, which differs for individuals with the same observable characteristics depending on the perception error about their relative position in the distribution. We find the value function for experienced utility to be concave for both positive and, at odds with prospect theory, also negative relative income. Loss aversion holds only for incomes that are sufficiently distant from the reference income. Our heterogeneity analysis shows that the slope of the value function is contingent on people’s personality, social beliefs, and how much they care about income comparisons.

Asymmetric micro-dynamics in spatial anonymous public goods game

A number of empirical studies have proved that human decision-making behaviors are bounded rational with external regulations and intrinsic motivations. In some situations, without information exchanges, an individual could make decisions only based on its own payoff, experience, memory and aspiration level. Such process can be theoretically expressed as the aspiration-driven dynamics applied in anonymous evolutionary games. On the other hand, from the perspective of behavioral economics and cognitive psychology, Prospect Theory qualitatively describes the bounded rationality of human decision-making behaviors under uncertain conditions. Here we explore a new approach to quantitatively construction of such bounded rationality by combining the aspiration updating rules in evolutionary games with the asymmetric utility value function in Prospect Theory. Monte Carlo simulations are carried out on a square lattice using the model of public goods game. The simulation results have shown that the level of cooperation at equilibrium states depends on the combined effects of synergy factor, individual greediness and sensitivity to gains and losses. Besides, the results give a reasonable explanation for the spontaneous emergence of cooperation among irrelevant individuals as well as the necessary conditions for the full-cooperation state. Furthermore, we argue that the study on human decision-making behaviors in groups requires more extensive and profound interdisciplinary researches.

Option Pricing with Greed and Fear Factor: The Rational Finance Approach

In this article, we explain main concepts of prospect theory and cumulative prospect theory within the rational dynamic asset pricing framework. We derive option pricing formulas when asset returns are altered by a generalized prospect theory value function or a modified Prelec’s weighting probability function. We introduce new parametric classes for prospect theory value functions and probability weighting functions consistent with rational dynamic pricing theory. After studying the behavioral finance notion of “greed and fear” from the perspective of rational dynamic asset pricing theory, we derive the corresponding option pricing formulas when asset returns follow continuous diffusions or discrete binomial trees. We define a mixed subordinated variance gamma process to model asset return and derive the corresponding option pricing formula. Finally, we apply the proposed probability weighting functions to study the greedy or fearful disposition of option traders when asset returns follow a mixed subordinated variance gamma process. The results indicate availability bias and diminishing sensitivity of option traders.

A simple non-parametric method for eliciting prospect theory's value function and measuring loss aversion under risk and ambiguity

Prospect theory emerged as one of the leading descriptive decision theories that can rationalize a large body of behavioral regularities. The methods for eliciting prospect theory parameters, such as its value function and probability weighting, are invaluable tools in decision analysis. This paper presents a new simple method for eliciting prospect theory’s value function without any auxiliary/simplifying parametric assumptions. The method is applicable both to choice under ambiguity (Knightian uncertainty) and risk (when events are characterized by objective probabilities). Our new elicitation method is implemented in a simple paper-and-pencil experiment (via an iterative multiple price list format). This is one of the first experiments that elicits non-parametric prospect theory’s value function with salient rewards. The collected data generally confirm findings in the existing literature: the value function is S-shaped (concave in the gain domain and convex in the loss domain) though there is a weaker loss aversion on the aggregate level and a substantial heterogeneity in loss aversion on the individual level (41% loss averse, 6% loss neutral and 53% gain seeking).

Model-free demand response scheduling strategy for virtual power plant considering risk attitude of consumer

Driven by the modern advanced information and communication technologies, distributed energy resources has the great potential for energy supply within the framework of virtual power plant(VPP). Meanwhile, demand response(DR) is becoming increasingly important for enhancing the VPP operation and mitigating the risks associated with the fluctuation of renewable energy resources(RESs). In this paper, we proposed an incentive-based DR program for VPP to minimize the deviation penalty from participating in power market. Markov decision process(MDP) with unknown transition probability is constructed from the VPP's prospective to formulate the incentive-based DR program, in which the randomness of consumer behavior and RES generation are taken into consideration. Furthermore, a value function of prospect theory(PT) is developed to characterize consumer's risk attitude and describe the psychological factors. A model-free deep reinforcement learning(DRL)-based approach is proposed to deal with the randomness existing in the model and adaptively determine the optimal DR pricing strategy for VPP, without requiring any system model information. Finally, the results of cases demonstrate the effectiveness of the proposed approach.

Method for product selection considering consumer’s expectations and online reviews

Purpose In recent years, the updating speed of products has been significantly accelerated, which not only provides diversified styles for consumers to select from but also makes consumers face selection problems sometimes. In addition, a large number of online reviews for products emerge on many e-commerce websites and influence consumers’ purchasing decisions. The purpose of this study is to propose a method for product selection considering consumer’s expectations and online reviews to support consumers’ purchasing decisions. Design/methodology/approach The product attributes are divided into two categories, i.e. demand attributes and word-of-mouth (WOM) attributes. For the demand attributes, for which the consumers can give specific quantified expectations, the value function of prospect theory is used to determine the consumer’s perceived values to the alternative products according to consumers’ expectations for these attributes and products’ specifications. For the WOM attributes, for which the consumers cannot give specific quantified expectations, the sentiment analysis method is used to identify the sentiment strengths for these attributes in the online reviews, and then the consumer’s perceived values to the alternative products are determined. On this basis, the product selection methods for single consumers and group consumers are given respectively. Findings Finally, taking the data of JD.com (https://www.jd.com/) as an example, the practicability and rationality of the method proposed in this paper is validated. Originality/value First, a new product selection problem considering consumer’s expectations and online reviews is extracted. Second, the product attributes are considered more comprehensively and are classified into two main categories. Third, the bounded rationality of the consumers in the decision-making process is described more reasonably. Fourth, the sentiment dictionaries for each WOM attribute are constructed and the algorithm step of identifying the sentiment strengths is designed, which can help to identify the sentiment strengths in the online reviews more accurately. Fifth, the situation that a group plans to purchase the same products and the members have inconsistent expectations for the product attributes is considered.

A New Method Based on PROMETHEE and TODIM for Multi-Attribute Decision-Making with Single-Valued Neutrosophic Sets

Single-valued neutrosophic sets (SVNSs) can effectively describe the multi-attribute decision-making (MADM) problems which are characterized by incompleteness and uncertainty. Aiming at the MADM problem of SVNSs, a series of methods are proposed to solve the problem, such as the TODIM and PROMETHEE methods. The main idea of the TODIM method is to establish a relative superiority function of scheme relative to other schemes based on the value function of prospect theory, and the ranking of alternatives is determined according to the obtained superiority. In the PROMETHEE method, the decision maker selects the preference function for each attribute according to their preference, and then calculates the priority index, inflow, outflow and net flow according to the difference of the attribute values of scheme, so as to determine the ranking of alternatives. In this paper, a new method based on PROMETHEE and TODIM is proposed to solve the MADM problem under the single-valued neutrosophic environment. Based on the calculation formula of inflow and outflow in PROMETHEE method, and the calculation formula of overall dominance in the TODIM method, a new integrated formula is obtained.

Sequential Route Choice Modeling Based on Dynamic Reference Points and Its Empirical Study

Aiming at the influence of information, we investigate and analyze the sequential route choice behavior under dynamic reference points based on cumulative prospect theory in this paper. An experiment platform collecting the sequential route choices based on C/S structure is designed and four types of information are released to participants, respectively. Real-time travel time prediction methods are then proposed for travelers’ decision-making. Using nonlinear regression method, the parameters of the value function and weight function of cumulative prospect theory are estimated under different types of information, respectively. It is found that travelers’ behavior showed obvious characteristic of risk pursuit under the circumstance where real-time travel time information is released. Instead, when they have access to descriptive information, they tend to be more conservative.

Reconciling Behavioral Finance and Rational Finance

In this paper, we explain main concepts of Prospect Theory and Cumulative Prospect Theory within the rational dynamic asset pricing framework. We derive option pricing formulas when asset returns are altered by a generalized Prospect Theory value function or a modified Prelec’s weighting probability function. We introduce new parametric classes for Prospect Theory value functions and probability weighting functions consistent with rational dynamic pricing theory. After the behavioral finance notion of “greed and fear” is studied from the perspective of rational dynamic asset pricing theory, we derive the corresponding option pricing formulas when asset returns follow continuous diffusions or discrete binomial trees. We define mixed subordinated variance gamma process to model asset return and derive the corresponding option pricing formula. Finally, we apply the proposed probability weighting functions to study the greedy or fearful disposition of option traders when asset returns follow a mixed subordinated variance gamma process. The results indicate availability bias and diminishing sensitivity of option traders.

Conditional Risk Premiums and the Value Function of Prospect Theory

This paper examines whether stock returns are consistent with the value function of prospect theory. We find that beta given a gain yields positive conditional premiums on returns while beta given a loss yields negative conditional premiums. This reflects the fact that the value function is concave for gains and convex for losses, implying risk-averse behavior for gains and risk-seeking behavior for losses respectively. Furthermore, the absolute value of the premiums is greater for losses, which is in line with the value function being steeper in this state. These new findings provide indication that investors behave according to prospect theory.

The Effect of Temporary Changes and Expectations on Individuals' Decisions: Evidence from a Tax Compliance Setting

ABSTRACTBased on prospect theory's value function, we predict how reference points adapt to influence individuals' tax evasion choices during and after experiencing temporary tax changes. Results from a multi-round experiment indicate reactions to temporary changes depend jointly on the direction of the change and expectations. Specifically, individuals experiencing a tax increase evade more while the increase is in effect. More interestingly, knowing, versus not knowing, a tax decrease is temporary prevents an increase in evasion after the temporary change expires, and may lead individuals to reduce evasion during the change. In a supplemental condition, we induce uncertainty by repeatedly extending a tax decrease. We find when uncertainty is introduced, both benefits of knowing the temporal nature of the decrease are lost. Overall results are consistent with individuals failing to adapt to a loss state and adapting quickly to a gain state unless they are certain the gain state is temporary.

The influence of demand response on wind-integrated power system considering participation of the demand side

Demand response (DR) can serve as virtual reserve to cope the impact of wind power on system reliability. This paper describes a new approach to investigating the impact of DR in a wind-integrated power system from the perspective of generation adequacy. First, owing to the uncertainty of human behavior, DR cannot be trusted to provide a sufficient reserve. To characterize the associated uncertainty, we use a value function of prospect theory to depict the risk attitude of the customer. Based on this function, we propose a variant Roth-Erev algorithm to characterize the uncertainty of customer participation and measure the available capacity of DR. Second, we introduce the available capacity of DR into operational constraints and construct a DR scheduling model to reduce system operation costs. Finally, based on the uncertainty characterization of DR and a scheduling model, we extend the traditional assessment procedure using Monte-Carlo simulation and propose a novel procedure to evaluate the impact of DR on generation adequacy. Simulation results show that introducing DR can improve the generation adequacy of a wind-integrated power system. The proposed DR scheduling method reduces the operational cost and improves generation adequacy.

Hesitant Fuzzy Linguistic Preference Utility Set and Its Application in Selection of Fire Rescue Plans.

Hesitant fuzzy linguistic term set provides an effective tool to represent uncertain decision information. However, the semantics corresponding to the linguistic terms in it cannot accurately reflect the decision-makers’ subjective cognition. In general, different decision-makers’ sensitivities towards the semantics are different. Such sensitivities can be represented by the cumulative prospect theory value function. Inspired by this, we propose a linguistic scale function to transform the semantics corresponding to linguistic terms into the linguistic preference values. Furthermore, we propose the hesitant fuzzy linguistic preference utility set, based on which, the decision-makers can flexibly express their distinct semantics and obtain the decision results that are consistent with their cognition. For calculations and comparisons over the hesitant fuzzy linguistic preference utility sets, we introduce some distance measures and comparison laws. Afterwards, to apply the hesitant fuzzy linguistic preference utility sets in emergency management, we develop a method to obtain objective weights of attributes and then propose a hesitant fuzzy linguistic preference utility-TOPSIS method to select the best fire rescue plan. Finally, the validity of the proposed method is verified by some comparisons of the method with other two representative methods including the hesitant fuzzy linguistic-TOPSIS method and the hesitant fuzzy linguistic-VIKOR method.

Goals as Reference Points in Marathon Running: A Novel Test of Reference Dependence

Although many empirical investigations have documented reference-dependent preferences, most studies of reference dependence have considered only status quo reference points. In a large-scale field study of marathon runners, we test whether goals, a non-status quo reference point, act similarly to status quo reference points. We find that satisfaction as a function of relative performance (the difference between a runner's time goal and her finishing time) exhibits loss aversion and diminishing sensitivity, consistent with the Prospect Theory value function. Unlike the Prospect Theory value function, however, we also find a discontinuity (or jump) at the reference point. We further find that loss aversion is moderated by goal importance, that multiple reference points simultaneously impact runner satisfaction, and that loss aversion is overestimated in predictions of satisfaction, but still present in actual experienced satisfaction.

Goals as reference points in marathon running: A novel test of reference dependence

Theories of reference-dependent preferences, such as Prospect Theory, imply that outcomes that are just below or just above a reference point are evaluated in a qualitatively distinct fashion. In a large-scale eld study of marathon runners, we test whether goals act as reference points in shaping the valuation of outcomes. Consistent with the Prospect Theory value function, we nd that satisfaction as a function of relative performance (the dierence between a runner’s time goal and her nishing time) exhibits loss aversion and diminishing sensitivity in both predictions of and actual experienced satisfaction. However, in contrast to the standard accounts of reference dependence, we observe that loss aversion is partially driven by a discontinuity or jump at the reference point. In addition, loss aversion is moderated by goal importance, with higher goal importance producing more loss aversion. Finally, we nd that a runner’s time goal as well as their previous marathon times simultaneously impact runner satisfaction, providing support for the impact of multiple reference points on satisfaction.

The Effect of Relative Concern on Life Satisfaction: Relative Deprivation and Loss Aversion

Income comparisons are important for individual well-being. We examine the shape of the relationship between relative income and life satisfaction, and test empirically if the features of the value function of prospect theory carry on to experienced utility. We draw on a unique dataset for a middle-income country, that allows us to work with an endogenous reference income, which differs for individuals with the same observable characteristics, depending on the perception error about their relative position in the distribution. We find the value function for experienced utility to be concave for both positive and, at odds with prospect theory, also negative relative income. Loss aversion is only satisfied for incomes that are sufficiently distant from the reference income. Our heterogeneity analysis shows that the slope of the value function differs across individuals who care differently about income comparisons, people with different personality traits, or social beliefs.