Framework Of Cumulative Prospect Theory Research Articles

Impact of the Local Dynamics on Exit Choice Behaviour in Evacuation Model

This study investigated the interplay between exit selection models and local pedestrian movement patterns within floor field frameworks. Specifically, this investigation analysed the performance of a multinomial logit exit choice model, incorporating both expected utility theory and cumulative prospect theory frameworks when coupled with three distinct local-level pedestrian movement models (FF-Von Neumann, FF-Moore, and NSFF). The expected utility theory framework considers the deterministic component as a linear relationship, while the cumulative prospect theory framework further considers the decision-maker’s risky attitudes by transforming objective terms into subjective terms using a power value function. The core objective was to comprehend how local movement dynamics, as represented by the floor field models, influence decision-making during exit selection. Comparative analyses revealed intriguing variations between the three local models, despite their shared expected utility theory-based exit choice framework. These discrepancies stemmed from the diverse pedestrian trajectory behaviours generated by each model. Consequently, these local dynamics impacted the decision-maker’s assessment of critical factors, such as the number of evacuees close to the decision-maker (NCDM) and the number of evacuees close to an exit (NCE), which the exit choice model incorporates. These assessments, in turn, significantly affected higher-level decision-making. The integration of the three models with the multinomial logit exit choice model, using either cumulative prospect theory and expected utility theory frameworks, further strengthened the observed bilateral relationship. While the specific nature of this relationship varied depending on the chosen framework and its implementation details, these consistent findings demonstrate the robustness of the results. This reinforced the influence of local-level pedestrian dynamics on higher-level exit selection, highlighting the importance of accurate crowd dynamics modelling, especially when advanced exit choice models consider local movement factors.

Risk preferences and refugee migration to Europe: An experimental analysis

Although the large majority of Syrians fleeing the civil war remain in neighbouring or nearby countries, others embark on hazardous land or sea crossings in pursuit of the uncertain prospect of obtaining refugee status in Europe. Understanding in what ways Syrian migrants who stay in nearby countries differ from those who seek asylum in Europe can help to better target European asylum policies. We address this issue by combining two experimental databases of refugees in Egypt and Luxembourg. First, we measure original risk preferences on the Egypt sample and show that Cumulative Prospect Theory (CPT) is better suited for modelling refugee behaviour under risk than Expected Utility Theory (EUT). Second, we compare the risk preference parameters of the two samples under the CPT framework and find that, on average, refugees in Egypt are more loss averse and overweight low probabilities more than their counterparts who migrated to Luxembourg. These results suggest a possible self-selection process among refugees migrating to Europe based on their risk preferences, which challenges current policy schemes.

A note on European farmers' preferences under cumulative prospect theory

AbstractExplaining farmer decision making using cumulative prospect theory is of increasing importance. We present a systematic review on European farmers' preferences under the cumulative prospect theory framework. We identified 17 studies covering 2324 farmers from 12 European countries. All studies report that (on average) farmers are: (i) risk averse, (ii) loss averse, and (iii) overweight small probabilities and underweight large probabilities. However, there is a large heterogeneity across and within studies. These findings have implications for the analysis and design of policy and insurance.

Do Risk Preferences Really Matter? The Case of Pesticide Use in Agriculture

Even if there exists an extensive literature on the modeling of farmers’ behavior under risk, actual measurements of the quantitative impact of risk aversion on input use are rare. In this article, we use simulations to quantify the impact of risk aversion on the optimal quantity of input and farmers’ welfare when production risk depends on how much of the input is used. The assumptions made on the technology and form of farmers’ risk preferences were chosen such that they are fairly representative of crop farming conditions in the USA and Western Europe. In our benchmark scenario featuring a traditional expected utility model, we find that less than 4% of the optimal pesticide expenditure is driven by risk aversion and that risk induces a decrease in welfare that varies from −1.5 to −3.0% for individuals with moderate to normal risk aversion. We find a stronger impact of risk aversion on quantities of input used when farmers’ risk preferences are modeled under the cumulative prospect theory framework. When the reference point is set at the median or maximum profit, and for some levels of the parameters that describe behavior toward losses, the quantity of input used that is driven by risk preferences represents up to 19% of the pesticide expenditure.

Risk-taking, resilience, and state anxiety during the COVID-19 pandemic: A coming of (old) age story

The current COVID-19 pandemic has created an unprecedented hostile psychological environment for individuals. Against the backdrop of this exogenous shock and applying a Cumulative Prospect Theory framework, we examined a relationship between risk-taking, trait resilience, and state anxiety, wherein age moderates the relationship between trait resilience and risk-taking, on state anxiety during the pandemic. We assess risk-taking using a behavioral measure and assess trait anxiety, big five personality traits, and other demographic factors in a sample of 515 individuals in the United States. Regression analysis revealed that age moderates the relationship between risk-taking and state anxiety and that highly resilient, risk-tolerant individuals experience lower state anxiety than less resilient risk-averse individuals. In contrast, older, more resilient, risk-averse individuals experience lower state anxiety than their younger, more resilient, risk-averse counterparts. Study limitations are noted, and additional research is suggested.

Behavioral portfolio insurance strategies

Portfolio insurance strategies that ensure a certain minimum portfolio value or floor such as the Constant Proportion Portfolio Insurance (CPPI) and the Option-based Portfolio Insurance are economically important and widely spread among the banking and insurance industries. In distress and volatile market environments, investors such as pension funds have a need to insure their portfolios against downside risk in order to meet certain future payments or liabilities. Non-anticipated shocks or negative interest rates, jumps, crashes, or overnight trading restrictions in stock prices could drop pension fund portfolios below desired levels (present value of pension obligations) making them underfunded with pension assets to pension liabilities ratio below 100%. In particular, within the current low interest rate environment, a high number of pension funds happen to be underfunded which is a severe practical problem. Because of such scenarios, there is a need for an investment strategy which covers both the case of funded and underfunded portfolios. This article introduces a novel strategy which generalizes the CPPI approach. It has the overall target of guaranteeing the investment goal or floor while participating in the performance of the assets and limiting the downside risk of the portfolio at the same time. We show that the strategy accounts for behavioral aspects of the investor such as distorted probabilities, a risk-averse behavior for gains, and a risk-seeking behavior for losses. The proposed strategy turns out to be optimal within the Cumulative Prospect Theory framework by Tversky and Kahneman (J Risk Uncertain 5(4):297–323, 1992).

Indistinguishability of small probabilities, subproportionality, and the common ratio effect

We show that, in the framework of Cumulative Prospect Theory, subproportionality as a property of the probability weighting function alone does not automatically imply the common ratio effect. This issue is particularly relevant for equal-mean lotteries because both risk-averse and risk-seeking behavior have to be predicted there. As a solution, we propose three simple properties of the probability weighting function which are sufficient to accommodate the empirical evidence on the common ratio effect for equal-mean lotteries for any S-shaped value function. These are (1) subproportionality, (2) indistinguishability of small probabilities, and (3) an intersection point with the diagonal lower than 0.5. While subproportionality and a fixed point lower than 0.5 are common assumptions in the literature, the property indistinguishability of small probabilities is introduced for the first time. The ratio of decision weights for infinitesimally small probabilities characterizes indistinguishability and is also an informative measure for the curvature of the probability weighting function at zero. The intuition behind indistinguishability is that, even though the ratio of probabilities stays constant, individuals tend to neglect this relative difference when probabilities get smaller.

Diminished Value Discrimination in Obsessive-Compulsive Disorder: A Prospect Theory Model of Decision-Making Under Risk.

Introduction: It has been hypothesized that people diagnosed with anxiety and obsessive-compulsive disorder (OCD) exhibit behavioral aberrations when faced with the potential for negative outcomes, but the specific cognitive aspects of decision-making that may be altered have not been systematically studied in clinical populations. Here, we studied decision-making in a clinical cohort using a task that allows for examination of the decision weights and values associated with different choice outcomes. Methods: Patients diagnosed with OCD (n = 10), generalized anxiety disorder (n = 15), social anxiety disorder (n = 14), and healthy controls (n = 20) were given a decision-making task and choices were modeled using a cumulative prospect theory framework. Results: We found OCD patients to have lower value discrimination than controls, as well as less optimal performance on the task, an effect that was mostly driven by trials with only positive outcomes. Discussion: Our results shed light on the cognitive processes that drive altered decision-making under risk in OCD. Specifically, they demonstrate that OCD patients have diminished sensitivity to positive outcomes, which might be associated with risk aversion and altered learning of gain. These findings also extend prior reports, suggesting that altered cognitive processing during decision-making is linked to altered perception of value, but not probability, in these patients.

Differences in Risk Preferences of the Main Ethnic Groups in Peninsular Malaysia: A Field Experiment

It is widely held that risk preferences differ between the three ethnic groups in Malaysia with the Chinese having the highest preference for risk and Malays having the lowest. This has been used to explain the Chinese preference for, and success in, business ventures relative to Malays. However, this assumption has never been tested in a controlled environment. Three hundred working adults from the three groups were recruited and participated in two-choice lottery games with real monetary reward and risk. The results were analysed using the framework of cumulative prospect theory. The outcomes indicate that broad generalisations regarding inter-ethnic risk tolerance are inaccurate. Malays were less risk averse than the Chinese or others when facing choices with the possibility of losing but became more risk averse only when facing choices with the possibility of winning. Malays were also more willing to take greater risk to reduce possible loss than to settle for a sure gain, compared to the others.

Stochastic Optimization in a Cumulative Prospect Theory Framework

Cumulative prospect theory (CPT) is a popular approach for modeling human preferences. It is based on probabilistic distortions and generalizes the expected utility theory. We bring the CPT to a stochastic optimization framework and propose algorithms for both estimation and optimization of CPT-value objectives. We propose an empirical distribution function-based scheme to estimate the CPT value, and then, use this scheme in the inner loop of a CPT-value optimization procedure. We propose both gradient based as well as gradient-free CPT-value optimization algorithms that are based on two well-known simulation optimization ideas: simultaneous perturbation stochastic approximation and model-based parameter search, respectively. We provide theoretical convergence guarantees for all the proposed algorithms and also illustrate the potential of CPT-based criteria in a traffic signal control application.

Over- and under-estimation of risks and counteractive adjustment for cold chain operations

PurposeThis study proposes the use of cumulative prospect theory (CPT) to predict over- and under-estimation of risks and the counteractive adjustment in a cold chain context. In particular, the purpose of this paper is to address the importance of the socio-demographic characteristics of an individual in influencing risk attitude and the analysis of measurable risk probability.Design/methodology/approachThis study uses CPT as the basis to develop a decision analysis model in which the two functions of value editing and probability weighting are nonlinear to adequately determine the flexible risk attitudes of individuals, as well as their prospects with numerous outcomes and different probabilities. An experiment was conducted to obtain empirical predictions, and an efficient Markov Chain Monte Carlo algorithm was applied to overcome the nonlinearity and dimensionality in the process of parameter estimation.FindingsThe respondents overweigh the minor cold chain risks with small probabilities and behave in a risk-averse manner, while underweighting major events with larger ones, thereby leading to risk-seeking behavior. Judgment distortion regarding probability was observed under risk decision with a low probability and a high impact. Moreover, the findings indicate that factors, such as gender, job familiarity and confidentiality significantly influence the risk attitudes and subjective probability weighting of the respondents.Research limitations/implicationsThe findings fit the framework of CPT and extend this theory to deal with human risk attitudes and subjective bias in cold chains. In particular, this study enhances the literature by providing an analysis of cold chain risk from both the human decision-making and managerial perspectives. Moreover, this research determined the importance of the socio-demographic characteristics of an individual to explain the variability in risk attitudes and responses.Practical implicationsManagers must consider the issues of flexible risk attitude and subjective judgment when making choices for risk mitigation strategies. Given the focus on counteractive adjustment for over- and under-estimated risk, firms could evaluate cold chain risk more accurately, and thereby enhance their resilience to risky events while reducing the variability of their performance.Originality/valueThe current study is the first to materialize the phenomena of over- and under-estimation of cold chain risks, as well as to emphasize the different characteristics for loss aversion and judgment distortion at the individual level.

An experimental study on cumulative prospect theory learning model of travelers’ dynamic mode choice under uncertainty

Abstract In this paper, we examined travelers’ dynamic mode choice behavior under travel time variability. We found travelers’ inconsistent risk attitudes through a binary mode choice experiment. Although the results deviated from the traditional utility maximization theory and could not be explained by the payoff variability effect, they could be well captured in a cumulative prospect theory (CPT) framework. After considering the imperfect memory effect, we found that the prediction ability of the cumulative prospect theory learning (CPTL) model could be significantly improved. The experimental results were also compared with the CPTL model and the reinforcement learning (REL) model. This study empirically showed the potential of alternative theories to better capture travelers’ day-to-day mode choice behavior under uncertainty. A new definition of willingness to pay (WTP) in a CPT framework was provided to explicitly consider travelers’ perceived value increases in travel time.

OPTIMAL INVESTMENT IN HEDGE FUNDS UNDER LOSS AVERSION

We study optimal investment problems in hedge funds for a loss averse manager under the framework of cumulative prospect theory. We obtain explicit solutions for a general utility function satisfying the Inada conditions and a piece-wise exponential utility function. Through a sensitivity analysis, we find that the manager reduces the risk of the hedge fund when her/his loss aversion, risk aversion, ownership in the fund, or management fee ratio increases. However, the increase of incentive fee ratio drives the manager to seek more risk in order to achieve higher prospect utility.

Optimal investment with transaction costs under cumulative prospect theory in discrete time

We study optimal investment problems under the framework of cumulative prospect theory (CPT). A CPT investor makes investment decisions in a single-period financial market with transaction costs. The objective is to seek the optimal investment strategy that maximizes the prospect value of the investor’s final wealth. We obtain the optimal investment strategy explicitly in two examples. An economic analysis is conducted to investigate the impact of the transaction costs and risk aversion on the optimal investment strategy.

Covered Call Writing in a Cumulative Prospect Theory Framework

The covered call writing, which entails selling a call option on one’s underlying stock holdings, is perceived by investors as a strategy with limited risk. It is a very popular strategy used by individual, professional and institutional investors; moreover, the CBOE developed the Buy Write Index which tracks the performance of a synthetic covered call strategy on the S&P500 Index. Previous studies analyze behavioral aspects of the covered call strategy, indicating that hedonic framing and risk aversion may explain the preference of such a strategy with respect to other designs. In this contribution, following this line of research, we extend the analysis and apply Cumulative Prospect Theory in its continuous version to the evaluation of the covered call strategy and study the effects of alternative framing

Travelers’ Risk-Taking Behaviors in Day-to-Day Dynamic Evolution Model

Uncertainties often exist in traffic systems because of interday route flow swapping and intraday road capacity degradation. These uncertainties obviously affect the traveler’s individual route adjustment behavior and the corresponding network traffic dynamic evolution at an aggregate level. Seeking to give a more realistic description of traffic dynamics, this study extends the existing day-to-day (DTD) model by considering both travelers’ study of uncertain travel time and travelers’ choice of risky routes. In the proposed model, an exponential-smoothing filter is introduced to describe travelers’ study of uncertain travel time. Meanwhile, on-time arrival probability is used to model travelers’ dynamic adjustment to their reference travel time (RTT). Under the framework of cumulative prospect theory, the perceived stochastic route travel time and the RTT are both integrated into a unified prospect value function to reflect travelers’ perception of route attractiveness. On this basis, a logit model is applied to describe travelers’ stochastic route choice behaviors. The proposed model’s several mathematical properties, including fixed-point existence, uniqueness, and stability, are also investigated through theoretical analyses. Numerical examples are used to illustrate the applications of the DTD model and verify some important dynamic system properties.

The role of numeracy and approximate number system acuity in predicting value and probability distortion.

It is well documented that individuals distort outcome values and probabilities when making choices from descriptions, and there is evidence of systematic individual differences in distortion. In the present study, we investigated the relationship between individual differences in such distortions and two measures of numerical competence, numeracy and approximate number system (ANS) acuity. Participants indicated certainty equivalents for a series of simple monetary gambles, and data were used to estimate individual-level value and probability distortion, using a cumulative prospect theory framework. We found moderately strong negative correlations between numeracy and value and probability distortion, but only weak and non-statistically reliable correlations between ANS acuity and distortions. We conclude that low numeracy contributes to number distortion in decision making, but that approximate number system acuity might not underlie this relationship.

Benefit distribution of private toll road: a cumulative prospect theory model with heterogeneous users

ABSTRACTThis paper examines how capacity and toll choices of the Build–Operate–Transfer mode affect the benefit distribution among private sector, road users and public under the framework of cumulative prospect theory. In the proposed network equilibrium model, we divide all road users into several classes differentiated by their valuation of travel time, and let the class-specific travel demand be endogenous. Our numerical results show that the benefit distribution is indeed influenced by the travellers' risk preference parameters significantly. Thus, administrators should carefully consider the travellers' risk attitude and their heterogeneity before determining whether or not to employ the Build–Operate–Transfer mode.

Influence of Parking on Train Station Choice under Uncertainty for park-and-ride Users

This paper presents a station choice model for park and ride (PnR) users based on uncertain parking attributes, such as parking search time (PST). In order to take into account uncertainty in PnR users’ choice process, a mixed logit model was developed within the framework of the discrete choice theory, the utility function in the model was established using a mean-variance approach under the cumulative prospect theory framework proposed Tversky and Kahneman [1]. A stated preference survey was designed for studying PnR users’ preference of stations, which was influenced by parking conditions at a train station. The experimental design was optimized using the D-optimality criterion. Our results show that the number that parking bays left in PnR facilities at given access time, parking cost including parking fees and fines and the variation of PST are important factors affecting PnR users’ station choice. PnR users were risk averse toward the variation of PST, which means that a PnR user is willing to choose a station with less uncertain or variation of PST.

Transit assignment based on stochastic user equilibrium with passengers perception consideration

Concerning the special nature of the transit network,the generalized path concept that maybe easily describe passenger route choice behavior was put forward.The key cost of each path was considered.Based on the analytical framework of cumulative prospect theory and passengers' perception,a stochastic user equilibrium assignment model was developed.A simple example revealed that the limitations of the traditional method can be effectively improved by this proposed method.The basic assumption of complete rationality in traditional model was improved.It helped us enhance our understanding of the complexity of urban public transportation behavior and the rule of decision-making.The facility layout and planning of the public transportation can be determined with this result,as well as the evaluation of the level of service.In addition,it can also be used as valid data support for traffic guidance.