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I show that stochastic contracts generate powerful incentives when agents suffer from probability distortion. When implementing these contracts, the principal can target probability distortions in order to inflate the agent's perceived benefits of exerting high levels of effort. This novel source of motivation is absent in contracts traditionally regarded as optimal. A theoretical framework and an experiment demonstrate that stochastic contracts implemented with small probabilities, which expose the agent to a high degree of risk, generate higher performance than cost‐equivalent contracts with lower or no risk exposure. I find that probability distortions that result from likelihood insensitivity—cognitive limitations that prevent the accurate evaluation of probabilities—account for this finding. The results highlight the limits of contracts traditionally regarded as optimal. [ABSTRACT FROM AUTHOR]

In order to estimate volatility-dependent probability weighting functions, we obtain risk neutral and physical densities from the Pan (J Financ Econ 63(1):3–50, 2002. https://doi.org/10.1016/S0304-405X(01)00088-5) stochastic volatility and jumps model. Across volatility levels, we find pronounced inverse S-shapes, i.e. small probabilities are overweighted, and probability weighting almost monotonically increases in volatility, indicating higher skewness preferences and crash aversion in volatile market environments. Moreover, by estimating probabilistic risk attitudes, equivalent to the share of risk aversion related to probability weighting, we shed further light on the pricing kernel puzzle. While pricing kernels estimated from the Pan (J Financ Econ 63(1):3–50, 2002. https://doi.org/10.1016/S0304-405X(01)00088-5) model display the typical U-shape as documented in the literature, pricing kernels—net of probability weighting—are strictly monotonically decreasing and thus in line with economic theory. Equivalently, we find risk aversion to be positive across wealth levels. Our results are robust to alternative maturities, wealth percentiles, alternative functional forms, a nonparametric empirical setting and variations of the Pan (J Financ Econ 63(1):3–50, 2002. https://doi.org/10.1016/S0304-405X(01)00088-5) coefficient estimates. [ABSTRACT FROM AUTHOR]

Under probability weighting, entrepreneurs with skewness preference tend to seek rightskewed and avoid left-skewed risks. We show that Chinese firms managed by CEOs with professional epidemic experience, i.e., who previously experienced the outbreak of SARS during their tenure as high level executives, have a lower stock price crash risk measured by the negative skewness of stock prices in subsequent periods. In particular, those firms intentionally avoid stock price crashes by adopting more conservative strategies in decisionmaking. Overall, we provide the first evidence on the unintended effect of entrepreneurs' subjective judgments of the probabilities of disease outbreaks on financial market stability. These have long-term implications for the financial system. [ABSTRACT FROM AUTHOR]

The empirical results on the influence of inexperience and experience in decision making are inconclusive. This paper offers a resolution to the puzzle of how empirical studies that advance contradictory risk-related claims can all command empirical support. The paper employs a paradigmatic model of decision making that examines two variables: (1) the decision maker's personality, of which inexperience and experience is one component; and (2) the particulars of the decision problem. These two variables permit us to resolve the puzzle of inconclusive empirical results by identifying the separating conditions under which each risk-related claim holds. [ABSTRACT FROM AUTHOR]

Recent computational psychiatric research has dissected decision-making under risk into different underlying cognitive computational constructs and identified disease-specific changes in these constructs. Studies are underway to investigate what kind of behavioral or psychological interventions can restore these cognitive, computational constructs. In our previous study, we showed that reminiscing about positive autobiographical memories reduced risk aversion and affected probability weighting in the opposite direction from that observed in psychiatric disorders. However, in that study, we compared positive versus neutral memory retrieval by using a within-subjects crossover posttest design. Therefore, the change of decision-making from baseline is unclear. Furthermore, we used a hypothetical decision-making task and did not include monetary incentives. We attempt to address these limitations and investigated how reminiscing about positive autobiographical memories influences decision-making under risk using a between-subjects pretest posttest comparison design with performance-contingent monetary incentives. In thirty-eight healthy, young adults, we found that reminiscing about positive memories reinforced the commonly observed inverted S-shaped nonlinear probability weighting (f = 0.345, medium to large in effect size). In contrast, reminiscing about positive memories did not affect risk aversion in general. Given that the change in probability weighting after reminiscing about positive memories is in the opposite direction from that observed in psychiatric disorders, our results indicate that positive autobiographical memory retrieval might be a useful behavioral intervention strategy for amending the altered decision-making under risk in psychiatric diseases. [ABSTRACT FROM AUTHOR]

Patients rely on knowing potential risks before accepting medical treatments, but risk perception can be distorted by cognitive biases and irrelevant information. We examined the interactive effects of subjective processes, objective knowledge, and demographic characteristics on how individuals estimate risks when provided with relevant and irrelevant probabilistic information. Participants read medical scenarios describing potential adverse effects associated with declining and accepting preventative treatment, as well as the objective likelihood of experiencing adverse effects associated with one of these two courses of action. We found that the perceived negativity of outcomes influenced perceptions of risk regardless of whether relevant probabilities were available and that the use of affect heuristics to estimate risk increased with age. Introducing objective estimates ameliorated age-related increases in affective distortions. Sensitivity to relevant probabilities increased with greater perceived outcome severity and was greater for men than for women. We conclude that relevant objective information may reduce the propensity to conflate outcome severity with likelihood and that medical judgments of risk vary depending on exposure to relevant and irrelevant probabilities. Implications for how medical professionals should communicate risk information to patients are considered. [ABSTRACT FROM AUTHOR]

Probability weighting refers to the behavioral bias in which irrational investors have a propensity to overweigh small probability tail events. In this study, we empirically investigate the asset pricing implications of probability weighting in commodity markets. We find that commodities with a high probability‐weighting value significantly underperform their low‐value pairs by 11% per annum. Neither conventional commodity risk factors nor existing characteristics explain this predictability. The predictability is more pronounced when arbitrage constraints are more binding. Commodities with a high probability‐weighting value also attract excess demand from non‐commercial traders. Collectively, these findings support a prospect theory‐based explanation for the cross‐section of commodity returns. [ABSTRACT FROM AUTHOR]

Does Subjective Evaluation of Probability Impact Asset Prices? The Nobel Prize–winning capital asset pricing model (CAPM) predicts that expected excess return of any asset is positively proportional to its exposure to the overall market: the beta, leading to an upward-sloping security market line. However, this prediction is contradicted by empirical studies that the return–beta slope is often flat or even downward-sloping, a puzzle called the "beta anomaly." The CAPM is premised upon the notion that market participants are all rational, including that they are able to objectively evaluate probabilities. However, evidence abounds that individuals are often unable to do so, examples being purchase of lottery tickets and insurance products, in which the extremely small probabilities of winning or losing big are exaggerated. This phenomenon of distorting probabilities at both tails is called "probability weighting" (PW), which is a key component of modern behavioral finance. The paper "Beta and Coskewness Pricing: Perspective from Probability Weighting" approaches the beta anomaly through PW. It offers an explanation of the beta anomaly via a new theoretical CAPM involving PW and an extensive empirical study. The security market line is often flat or downward-sloping. We hypothesize that probability weighting plays a role and one ought to differentiate between periods in which agents overweight extreme events and those in which they underweight them. Overweighting inflates the probability of extremely bad events and demands greater compensation for beta risk, whereas underweighting does the opposite. Unconditional on probability weighting, these two effects offset each other, resulting in a flat or slightly negative return–beta relationship. Similarly, overweighting the tails enhances the negative relationship between return and coskewness, whereas underweighting reduces it. We derive a three-moment conditional capital asset pricing model for a market with rank-dependent utility agents to make these predictions, and we support our theory through an extensive empirical study. Funding: This work was supported by National Natural Science Foundation of China [Grants 71971083, 71931004, 72171138]; Program for Innovative Research Team of Shanghai University of Finance and Economics [Grant 2020110930]; Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science-Ministry of Education, East China Normal University; a start-up grant and the Nie Center for Intelligent Asset Management at Columbia University. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2421. [ABSTRACT FROM AUTHOR]

We provide a comprehensive analysis of the impact of probability weighting on optimal insurance demand in a unified framework. We identify decreasing relative overweighting as a new local condition on the probability weighting function that is useful for comparative static analysis. We discuss the effects of probability weighting on coinsurance, deductible choice, insurance demand for low-probability, high-impact risks versus high-probability, low-impact risks, and insurance demand in the presence of nonperformance risk. Probability weighting can make better or worse predictions than expected utility depending on the insurance demand problem at hand. [ABSTRACT FROM AUTHOR]

We report experimental data from standard market entry games and winner-take-all games. At odds with traditional decision-making models with risk aversion, the winner-take-all condition results in substantially more entry than the expected-payoff-equivalent market entry game. We explore three candidate explanations for excess entry: blind spot, illusion of control, and joy of winning, none of which receive empirical support. We provide a novel theoretical explanation for excess entry based on cumulative prospect theory and test it empirically. Our results suggest that excess entry into highly competitive environments is not caused by a genuine preference for competing, but is instead driven by probability weighting. Market entrants overweight the small probabilities associated with the high payoff outcomes in winner-take-all markets, while they underweight probable failures. This paper was accepted by Yan Chen, behavioral economics and decision analysis. Funding: This work was supported by the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung [Grants 100018_182185 and 26022621] and the Dr. h.c. Emil Zaugg-Fonds [Grant B11162135]. Supplemental Material: The data files and e-companion are available at https://doi.org/10.1287/mnsc.2022.4397. [ABSTRACT FROM AUTHOR]

The literature suggests that probability weighting and choice set dependence influence risky choices. However, their relative importance remains an open question. We present a joint test that uses binary choices between lotteries provoking Common Consequence and Common Ratio Allais Paradoxes and manipulates their joint payoff distribution. We show non-parametrically that probability weighting and choice set dependence both play a role at describing aggregate choices. To parsimoniously account for heterogeneity, we also estimate a structural model using a finite mixture approach. The model uncovers substantial heterogeneity and classifies subjects into three types: 38% Prospect Theory types whose choices are predominantly driven by probability weighting, 34% Salience Theory types whose choices are predominantly driven by choice set dependence, and 28% Expected Utility Theory types. The model predicts type-specific differences in the frequency of preference reversals out-of-sample, i.e., in choices with a different context than the ones used for estimating the model. Moreover, the out-of-sample predictions indicate that the choice context shapes the influence of choice set dependence. [ABSTRACT FROM AUTHOR]

Psychiatric disorders such as depressive and anxiety disorders are associated with altered decision-making under risk. Recent advances in neuroeconomics and computational psychiatry have further discomposed risk-based decision-making into distinct cognitive computational constructs and showed that there may be disorder-specific alterations in these constructs. As a result, it has been suggested these cognitive computational constructs may serve as useful behavioral biomarkers for these disorders. However, to date, little is known about what psychological or behavioral interventions can help to reverse and manage the altered cognitive computational constructs underlying risk-based decision-making. In the present study, we set out to investigate whether recalling positive autobiographical memories may affect risk-based decision-making in healthy volunteers using a description-based task. Specifically, based on theories of behavioral economics, we dissected risk preference into two cognitive computational constructs, utility sensitivity and probability weighting. We found that compared to recalling neutral memories, retrieving positive autobiographical memories increased utility sensitivity (Cohen's d = 0.447), indicating reduced risk aversion. Meanwhile, we also tested the influence of memory retrieval on probability weighting, the effect, however, was unreliable and requires further in-depth investigation. Of clinical relevance, the change in risk aversion after recalling positive memories was in the opposite direction compared to those reported in psychiatric disorders. These results argue for the potential therapeutic effect of positive autobiographical memory retrieval for the amendment of altered risk-based decision-making in psychiatric disorders. [ABSTRACT FROM AUTHOR]

Promoting prevention is an important goal of public policy. Fifty years ago, Ehrlich and Becker (J Polit Econ 80:623–648, 1972) proposed a simple model of prevention (or self-protection as they called it). Surprisingly enough, subsequent research, mainly within the expected utility paradigm, showed that it is hard to derive clear predictions within this simple model that can help to guide policy. This is what I refer to as the prevention puzzle: why is it so hard for economic theory to guide prevention decisions? In this article I try to shed light on this question. I review the existing literature and add some tentative new results under nonexpected utility. While the impact of risk aversion on prevention is complex, three factors seem to contribute unambiguously to underprevention: prudence, likelihood insensitivity, and loss aversion. I conclude by giving some ideas how empirical research may contribute to the understanding of prevention decisions and help to solve the prevention puzzle. [ABSTRACT FROM AUTHOR]

Probability weighting is a major concept for accommodating systematic departures from expected utility theory. We examine the relation between probability weighting and cognitive ability with two experiments: one recruiting subjects with a large variation in cognitive ability and the other using the within-subject manipulation of time constraints in lottery choices and cognitive tests. We find a significant association between likelihood insensitivity—the cognitive component of probability weighting—and cognitive limitation such that subjects with a lower cognitive score or more interrupted cognition due to time pressure respond less discriminately to intermediate probabilities and more over-sensitively to extreme probabilities. Our findings shed light on the sources of anomalous choices against expected utility theory. This paper was accepted by Yan Chen, behavioral economics and decision analysis. [ABSTRACT FROM AUTHOR]

This paper reports two experiments in which attitudes toward temporal risk resolution is elicited from choices between two-outcome lotteries that pay out at some future fixed date and can be resolved either now or later. We show that matching probabilities provides a simple method to measure attitudes toward temporal resolution—via the utility scale—under the recursive expected utility of Kreps and Porteus. We also analyze our data using a general recursive model that can reveal attitudes toward temporal risk resolution through the utility scale and/or the probability weighting scale. In terms of goodness of fit, as well as of prediction accuracy, our results point to a better performance of the probability weighting approach. More specifically, we show that individuals become less sensitive and more pessimistic with respect to winning probabilities when lotteries are resolved later rather than now. This paper was accepted by George Wu, decision analysis. [ABSTRACT FROM AUTHOR]

Prevention efforts, such as quitting smoking, flu vaccination, and exercising, are of crucial importance in health policy, but people tend to undertake too few of them. The main reason is that most prevention efforts only reduce but do not completely eliminate the risk of poor health. This makes it harder for people to assess the benefits of prevention, because they tend to misperceive and transform probabilities. In "When Risk Perception Gets in the Way: Probability Weighting and Underprevention," Baillon et al. introduce psychological insights (probability weighting) in a model of optimal decision making and show that most people undertake too little prevention when the risk of poor health is between 10% and 80%. The paper discusses several policy measures to make people spend more on prevention. Personal decisions about health hazards are the main cause of impaired health and premature death. People smoke and eat too much, and they exercise too little. The lack of preventive efforts is surprising given their proven effectiveness. In the early 1960s, Arrow suggested that moral hazard might be a reason for underprevention, but this explanation was later challenged. In this paper, we show that underprevention might be caused by misperceived probabilities. We derive when and how probability weighting gets in the way of prevention by blurring its benefits. We use a general model of prevention, encompassing several special cases from the literature. We also show how perceived ambiguity makes the problem of underprevention even worse by amplifying the effect of probability weighting. [ABSTRACT FROM AUTHOR]

Both depressive and anxiety disorders have been associated with excessive risk avoidant behaviors, which are considered an important contributor to the maintenance and recurrence of these disorders. However, given the high comorbidity between the two disorders, their independent association with risk preference remains unclear. Furthermore, due to the involvement of multiple cognitive computational factors in the decision-making tasks employed so far, the precise underlying mechanisms of risk preference are unknown. In the present study, we set out to investigate the common versus unique cognitive computational mechanisms of risk preference in depression and anxiety using a reward-based decision-making task and computational modeling based on economic theories. Specifically, in model-based analysis, we decomposed risk preference into utility sensitivity (a power function) and probability weighting (the one-parameter Prelec weighting function). Multiple linear regression incorporating depression (BDI-II) and anxiety (STAI state anxiety) simultaneously indicated that only depression was associated with one such risk preference parameter, probability weighting. As the symptoms of depression increased, subjects' tendency to overweight small probabilities and underweight large probabilities decreased. Neither depression nor anxiety was associated with utility sensitivity. These associations remained even after controlling covariates or excluding anxiety-relevant items from the depression scale. To our knowledge, this is the first study to assess risk preference due to a concave utility function and nonlinear probability weighting separately for depression and anxiety using computational modeling. Our results provide a mechanistic account of risk avoidance and may improve our understanding of decision-making deficits in depression and anxiety. [ABSTRACT FROM AUTHOR]

Current decision‐making models assume that an individual's attitude towards risk is unique. Hence, a decision maker's processing of probabilities and the resulting degree of probability weighting should not vary within the domain of risk. This paper provides evidence that challenges this assumption. We conduct two experiments involving different gambles, that is, risky games where objective probabilities are known, no further information‐based advantages exist, and outcomes are independent of knowledge. Even though all probabilities are explicitly provided, we find that individuals exhibit more pronounced inverse‐S‐shaped probability weighting if they perceive their level of expertise regarding a gamble to be lower. This result suggests that individuals are subject to ignorance illusion in decisions under risk, constituting expertise‐dependent risk attitudes. We document that ignorance illusion stems from the wrongly assigned importance of perceived expertise in the decision‐making process and that it occurs in both the gain and the loss domain. [ABSTRACT FROM AUTHOR]

We analyze the impact of short-run (90 days) and long-run (30 years) earthquake risk on real estate transaction prices in five Japanese cities (Tokyo, Osaka, Nagoya, Fukuoka, and Sapporo), using quarterly data over the period 2006–2015. We exploit a rich panel dataset (331,343 observations) with property characteristics, ward attractiveness information, macroeconomic variables, and long-run seismic hazard data, supplemented with short-run earthquake probabilities generated from a seismic excitation model using historical earthquake occurrences. We design a hedonic property price model that allows for subjective probability weighting, employ a multivariate error components structure, and develop associated maximum likelihood estimation and variance computation procedures. Our approach enables us to identify the total compensation for earthquake risk embedded in property prices, to decompose this into pieces stemming from short-run and long-run risk, and to distinguish between objective and subjectively weighted ("distorted") earthquake probabilities. We find that objective long-run earthquake probabilities have a statistically significant negative impact on property prices, whereas short-run earthquake probabilities become statistically significant only when we allow them to be distorted. The total compensation for earthquake risk amounts to an average –2.0% of log property prices, slightly more than the annual income of a middle-income Japanese household. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

How do people distribute defenses over a directed network attack graph, where they must defend a critical node? This question is of interest to computer scientists, information technology and security professionals. Decision-makers are often subject to behavioral biases that cause them to make sub-optimal defense decisions, which can prove especially costly if the critical node is an essential infrastructure. We posit that non-linear probability weighting is one bias that may lead to sub-optimal decision-making in this environment, and provide an experimental test. We find support for this conjecture, and also identify other empirically important forms of biases such as naive diversification and preferences over the spatial timing of the revelation of an overall successful defense. The latter preference is related to the concept of anticipatory feelings induced by the timing of the resolution of uncertainty. [ABSTRACT FROM AUTHOR]

I study the effect of task difficulty on workers' effort. I find that task difficulty has an inverse-U effect on effort and that this effect is quantitatively large, especially when compared to the effect of conditional monetary rewards. Difficulty acts as a mediator of monetary rewards: conditional rewards are most effective at the intermediate or high levels of difficulty. The inverse-U pattern of effort response to difficulty is inconsistent with many popular models in the literature, including the Expected Utility models with the additively separable cost of effort. I propose an alternative mechanism for the observed behavior based on non-linear probability weighting. I structurally estimate the proposed model and find that it successfully captures the behavioral patterns observed in the data. I discuss the implications of my findings for the design of optimal incentive schemes for workers and for the models of effort provision. [ABSTRACT FROM AUTHOR]

Probability weighting is a marked feature of decision-making under risk. For poor people in rural areas of developing countries, how probabilities are evaluated matters for livelihoods decisions, especially the probabilities associated with losses. Previous studies of risky choice among poor people in developing countries seldom consider losses and do not offer a refined tracking of the probability-weighting function (PWF). We investigate probability weighting among smallholder farmers in Uganda, separately for losses and for gains, using a method (common consequence ladders) that allows refined tracking of the PWF for a population with low levels of literacy. For losses, we find marked probability weighting near zero, which is in line with evidence found in Western labs. For gains, the absence of probability weighting is remarkable, particularly its absence near 100%. We also find marked differences in probability weighting for traditional farmers which are in line with the observed livelihoods strategies in the study area. [ABSTRACT FROM AUTHOR]

The analysis of alternative decisions and the choice of the optimal – in a given sense – decision is an integral part of people’s purposeful activity in all areas of their social life. Many formal approaches have been proposed to solve these problems. One such approach is expected utility theory, which correctly models individuals’ subjective preferences and attitudes to risk. For a very long time this theory was the leading approach for decision making under conditions of risk. However, numerous practical studies have shown its weakness: the theory did not explicitly use subjective perceptions of decision outcome probabilities in optimal decision-making processes. This research has led to the creation and development of approaches to explicitly consider the probabilities of outcomes in decision making. This paper provides a critical analysis of the descriptive properties of expected utility theory and presents various forms of probability weighting functions. [ABSTRACT FROM AUTHOR]

We study portfolio selection in a complete continuous‐time market where the preference is dictated by the rank‐dependent utility. As such a model is inherently time inconsistent due to the underlying probability weighting, we study the investment behavior of a sophisticated consistent planners who seek (subgame perfect) intra‐personal equilibrium strategies. We provide sufficient conditions under which an equilibrium strategy is a replicating portfolio of a final wealth. We derive this final wealth profile explicitly, which turns out to be in the same form as in the classical Merton model with the market price of risk process properly scaled by a deterministic function in time. We present this scaling function explicitly through the solution to a highly nonlinear and singular ordinary differential equation, whose existence of solutions is established. Finally, we give a necessary and sufficient condition for the scaling function to be smaller than one corresponding to an effective reduction in risk premium due to probability weighting. [ABSTRACT FROM AUTHOR]

While much literature has focused on preferences regarding risk, preferences over skewness also have significant economic implications. An important and understudied aspect of skewness preferences is how they affect risk taking. In this paper, we design a novel laboratory experiment that elicits certainty equivalents over lotteries where the variance and skewness of the outcomes are orthogonal to each other. This design enables us to cleanly measure both skewness seeking/avoiding and risk taking behavior, and their interaction, without needing to make parametric assumptions. Our experiment includes both left- and right-skewed lotteries. The results reveal that the majority of subjects are skewness avoiding risk takers who correspondingly also take more risk when facing less skewed lotteries. Our second contribution is to link these choices to individual rank-dependent utility preference parameters estimated using a separate lottery choice protocol. Using a latent-class model, we are able to identify two classes of subjects: skewness avoiders with the classic inverse s-shaped probability weighting function and skewness neutral subjects that do not have an inverse s-shaped probability weighting function. Our results thus demonstrate the link between probability distortion and skewness seeking/avoidance choices. They also highlight the importance of accounting for individual heterogeneity. [ABSTRACT FROM AUTHOR]

Odors are strong elicitors of affect, and they play an important role in guiding human behavior, such as avoiding fire or spoiled food. However, little is known about how risky decision making changes when stimuli are olfactory. We investigated this question in an experimental study of risky decision making with unpleasant odors and monetary losses in a fully incentivized task with real outcomes. Odor and monetary decisions were matched so that monetary losses corresponded to the amount of money participants were willing to pay to avoid smelling an odor. Hierarchical Bayesian analyses using prospect theory show that participants were less sensitive to probabilities when gambling with odors than when gambling with money. These results highlight the importance of taking the sensory modality into account when studying risky decision making. [ABSTRACT FROM AUTHOR]

A recent strand of the literature on decision-making under uncertainty has pointed to an intriguing behavioral gap between decisions made from description and decisions made from experience. This study reinvestigates this description-experience gap to understand the impact that sampling experience has on decisions under risk. Our study adopts a complete sampling paradigm to address the lack of control over experienced probabilities by requiring complete sampling without replacement. We also address the roles of utilities and ambiguity, which are central in most current decision models in economics. Thus, our experiment identifies the deviations from expected utility due to over- (or under-) weighting of probabilities. Our results confirm the existence of the behavioral gap, but they provide no evidence for the underweighting of small probabilities within the complete sampling treatment. We find that sampling experience attenuates rather than reverses the inverse S-shaped probability weighting under risk. [ABSTRACT FROM AUTHOR]

We assume that the ex post utility of a regret-sensitive agent facing a menu of lotteries depends upon the payoff of the chosen lottery in the realized state together with the forgone best payoff available in the menu in that state. If two lotteries in the menu have the same distribution of payoffs, the one whose payoff is less statistically concordant with the best alternative yields a larger risk of regret, which should be rejected by regret-risk-averse individuals. This means that regret-risk aversion is equivalent to the supermodularity of the bivariate utility function. We define regret-risk aversion in the small and in the large. We also show that regret-risk aversion tends to induce a bias in favor of the risky act in any one-risky-one-safe menu, in particular when the payoff of the risky choice is highly positively skewed. This is compatible with the "possibility effect" that is well documented in prospect theory. Symmetrically, we define the aversion to rejoicing-risk that can prevail when the ex post utility is alternatively sensitive to the forgone worst payoff. We show that rejoicing-risk-seeking is compatible with the "certainty effect". We finally show that regret-risk-averse and rejoicing-risk-seeking people behave as if they had rank-dependent utility preferences with an inverse-S shaped probability weighting function that reproduces estimates existing in the literature. [ABSTRACT FROM AUTHOR]

We propose a test of the theory of skewness preferences. The probability weighting feature that is the basis of their theory relies on investors overweighting the probability of extreme, positive returns. The resulting investor preferences for positive skewness in return distributions will lead to excess demand, contemporaneous price premiums, and negative expected returns. We use the well-documented 52-week high bias as a method to truncate investors' weighted probability of expected right-tail events. We find evidence supporting the theoretical framework of Barberis and Huang as the negative return premiums associated with positive skewness is driven almost entirely by stocks that are farther away from the their 52-week high. No negative premiums related to skewness are detected when stock prices are close to the 52-week high. [ABSTRACT FROM AUTHOR]

In this paper we estimate the pricing kernel from the Hong Kong index option market and obtain the empirical probability weighting functions based on the rank-dependent expected utility. The empirical pricing kernel is estimated semi-parametrically as the ratio of the risk-neutral and objective densities. We employ a two-step estimation procedure to estimate the objective and risk-neutral densities under a consistent parametric framework of the non-affine generalised autoregressive conditional heteroskedasticity (G.A.R.C.H.) diffusion model. In the first step, we develop a continuous particle filters-based maximum likelihood estimation method to estimate the objective parameters of the G.A.R.C.H. diffusion model using the Hang Seng Index (H.S.I.) returns. In the second step of our estimation, we depart from the usual pure calibration approach and use the H.S.I. option prices to estimate the risk-neutral parameters of the G.A.R.C.H. diffusion model by constraining certain parameters to be consistent with the time-series behaviour of H.S.I. returns. Based on the estimated objective and risk-neutral parameters, the objective and risk-neutral densities are obtained by inverting the corresponding characteristic functions. Empirical results indicate that the empirical pricing kernel estimated from the Hong Kong index option market is non-monotonic and the estimated probability weighting functions are S-shaped, which implies that investors underweight small probability events and overweight large ones. [ABSTRACT FROM AUTHOR]

In a paper published in Management Science in 2015, Stewart, Reimers, and Harris (SRH) demonstrated that shapes of utility and probability weighting functions could be manipulated by adjusting the distributions of outcomes and probabilities on offer as predicted by the theory of decision by sampling. So marked were these effects that, at face value, they profoundly challenge standard interpretations of preference theoretic models in which such functions are supposed to reflect stable properties of individual risk preferences. Motivated by this challenge, we report an extensive replication exercise based on a series of experiments conducted as a quasi-adversarial collaboration across different labs and involving researchers from both economics and psychology. We replicate the SRH effect across multiple experiments involving changes in many design features; importantly, however, we find that the effect is also present in designs modified so that decision by sampling predicts no effect. Although those results depend on model-based inferences, an alternative analysis using a model-free comparison approach finds no evidence of patterns akin to the SRH effect. On the basis of simulation exercises, we demonstrate that the SRH effect may be a consequence of misspecification biases arising in parameter recovery exercises that fit imperfectly specified choice models to experimental data. Overall, our analysis casts the SRH effect in an entirely new light. This paper was accepted by Yuval Rottenstreich, judgment and decision making [ABSTRACT FROM AUTHOR]

Experimental studies suggest that individuals exhibit more risk aversion in choices among prospects when the payment and resolution of uncertainty are immediate relative to when it is delayed. This leads to preference reversals that cannot be attributed to discounting. When data suggest that utility is time-independent, probability weighting functions, such as those used to model prospect theory preferences, can accommodate such reversals. We propose a simple descriptive model with a two-parameter probability weighting function where one of these parameters depends on the time at which a prospect is resolved. The time-dependent parameter is responsible for the curvature of the probability weighting function and is regarded as an index of (in)sensitivity towards changes in probabilities. We provide conditions that characterize increased sensitivity towards more distant probabilities; this can account for the observed relatively less risk aversion towards delayed prospects. In our framework, the discount function is unrestricted, such that the model is compatible with empirical findings of non-constant discounting. In a simple application to bargaining we illustrate when it is advantageous for an individual to advance or delay the bargaining resolution time if an opponent displays increased sensitivity towards probability changes with delay. [ABSTRACT FROM AUTHOR]

We study Arrow–Debreu equilibria for a one‐period‐two‐date pure exchange economy with rank‐dependent utility agents having heterogeneous probability weighting and outcome utility functions. In particular, we allow the economy to have a mix of expected utility agents and rank‐dependent utility ones, with nonconvex probability weighting functions. The standard approach for convex economy equilibria fails due to the incompatibility with second‐order stochastic dominance. The representative agent approach devised in Xia and Zhou (2016) does not work either due to the heterogeneity of the weighting functions. We overcome these difficulties by considering the comonotone allocations, on which the rank‐dependent utilities become concave. Accordingly, we introduce the notion of comonotone Pareto optima, and derive their characterizing conditions. With the aid of the auxiliary problem of price equilibria with transfers, we provide a sufficient condition in terms of the model primitives under which an Arrow–Debreu equilibrium exists, along with the explicit expression of the state‐price density in equilibrium. This new, general sufficient condition distinguishes the paper from previous related studies with homogeneous and/or convex probability weightings. [ABSTRACT FROM AUTHOR]

Our understanding of the decisions made under scenarios where both descriptive and experience-based information are available is very limited. Underweighting of small probabilities was observed in the gain domain when both description and experience were provided. The divergence observed from the prospect theory suggests a need for a separate or modified theory of decision making under risk. Recent studies suggest a possible role of probability weighting in the choice behavior under risk. We investigated both gain and loss domains with and without feedback for small and large probability conditions. We characterized the shape of the probability weighting function by a two-parameter functional form representing discriminability (concave-convex shape) and attractiveness (level of absolute weights relative to objective probability). We replicated a fourfold pattern of risk attitude on non-WEIRD population. We find that feedback leads to underweighting of small probabilities and overweighting of large probabilities in the gain domain and overall underweighting of probabilities in the loss domain. We find that underweighting of small probabilities is driven by changes in discriminability and attractiveness components in the gain domain and changes in the attractiveness component in the loss domain. We have interpreted the results by proposing an updated belief-based account of decisions under uncertainty in which feedback, when available, influences the probability weighting mediating the choice behavior. [ABSTRACT FROM AUTHOR]

This paper provides experimental evidence of the role of higher order risk attitudes—especially prudence—in prevention behavior. Prudence, under an expected utility framework, increases (decreases) self-protection effort compared to the risk neutral level when the risk of losing part of an income exists in a future (the same) period. Motivated by these predictions that give the exact test on prudence, an experiment was designed where subjects go through higher order risk attitude elicitation and make a self-protection decision. In contrast to the expected utility theory, the observed efforts are less than the risk neutral level, regardless of the timing of loss. This violation of expected utility predictions can be explained by probability weighting. [ABSTRACT FROM AUTHOR]

We investigate decisions in the face of emergency situations where potential consequences include loss of life, for example, the choice of methods to rescue a group of people who are trapped in a fire. In particular, we conduct two sets of experiments to depict public risk preferences for potential fatalities in a rescue mission. The first set of experiments asks binary questions on a collection of hypothetical emergency scenarios such as fires, air crashes, and marine accidents. Our results show that people are inclined to choose risky options in emergency situations, indicating risk-seeking behavior. However, we observe no significant decline in the subjects' willingness to save one more life as the base number of people in danger increases, which contradicts the risk-seeking utility function implied by expected utility theory. We then conduct the second set of experiments to elicit possible distortions of probabilities in addition to the value function of fatalities under prospect theory. The value functions of most subjects are concave with increasing marginal effect of losing one more life, and most subjects deflate the probability of an adverse event no matter whether the probability is small or large. We compare our results with prospect theory studies involving money and time in the loss domain, and provide possible explanations for the observed discrepancies. [ABSTRACT FROM AUTHOR]

The paper reviews the development of von Neumann and Morgenstern (vNM) utility theory. Kahneman and Tversky’s (KT’s) prospect theory is introduced. The vNM utility function is compared and contrasted with KT’s value function. We prove the uniqueness of two popular utility functions. First, we show that all power utility functions possess constant RRA. And, we show that all exponential utility functions have constant ARA. The paper concludes by discussing applications, strengths and weaknesses of various utility functions. [ABSTRACT FROM AUTHOR]

In this paper we analyze how changes in inverse S-shaped probability weighting influence optimal portfolio choice in a rank-dependent utility model. We derive sufficient conditions for the existence of an optimal solution of the investment problem, and then define the notion of a more inverse S-shaped probability weighting function. We show that an increase in inverse S-shaped weighting typically leads to a lower allocation to the risky asset, regardless of whether the return distribution is skewed left or right, as long as it offers a non-negligible risk premium. Only for lottery stocks with poor expected returns and extremely positive skewness does an increase in inverse S-shaped probability weighting lead to larger portfolio allocations. [ABSTRACT FROM AUTHOR]

In comparing different risk elicitation methods under the assumptions of expected utility theory, previous studies have found significant differences in the elicited risk attitudes. This paper extends this line of research to consider cumulative prospect theory by comparing risk attitudes and probability weightings determined using two elicitation methods: the method by Tanaka et al. (Am Econ Rev 100(1):557-571, 2010; TCN method) and the method by Wakker and Deneffe (Manage Sci 42(8):1131-1150, 1996; WD method). We demonstrate that the two methods reveal significantly different mean values for the measured risk attitudes. Participants are classified on average as moderately risk-averse using the TCN method, whereas the same individuals are classified as nearly risk-neutral using the WD method. Moreover, we find that on average, participants overweight low probabilities and underweight high probabilities to a greater extent with the WD method than with the TCN method. Therefore, the different elicitation methods, that both consider probability weighting, can lead to different measured values of risk attitude and probability weighting. [ABSTRACT FROM AUTHOR]

First, this paper introduces and axiomatizes range-dependent utility as a new conceptual framework for decision making under risk. It is a simple and well-defined generalization of expected utility theory in which utility depends on the range of lottery outcomes. Second, a special case of this framework is proposed for prediction. It is based on applying a single utility function (decision utility) to every normalized lottery range. The resultant decision utility model predicts well-known expected utility paradoxes without recourse to probability weighting. Necessary and sufficient conditions for the model to satisfy monotonicity with respect to first-order stochastic dominance are identified. The typical decision utility function, which is confirmed by both experimental data and normative considerations, is S shaped. [ABSTRACT FROM AUTHOR]

How much do different monetary and non-monetary motivators induce costly effort? Does the effectiveness line up with the expectations of researchers and with results in the literature? We conduct a large-scale real-effort experiment with eighteen treatment arms. We examine the effect of (1) standard incentives; (2) behavioural factors like social preferences and reference dependence; and (3) non-monetary inducements from psychology. We find that (1) monetary incentives work largely as expected, including a very low piece rate treatment which does not crowd out effort; (2) the evidence is partly consistent with standard behavioural models, including warm glow, though we do not find evidence of probability weighting; (3) the psychological motivators are effective, but less so than incentives. We then compare the results to forecasts by 208 academic experts. On average, the experts anticipate several key features, like the effectiveness of psychological motivators. A sizeable share of experts, however, expects crowd-out, probability weighting, and pure altruism, counterfactually. As a further comparison, we present a meta-analysis of similar treatments in the literature. Overall, predictions based on the literature are correlated with, but underperform, the expert forecasts. [ABSTRACT FROM AUTHOR]

A rapidly exploding body of recent literature recognizes the limitations of modeling travel behavior with the assumption that the traveler faces no risk. More recent models incorporate risk and can be based on expected utility theory (EUT). However, violations of key assumptions of EUT have led to the development of non-EUT models of behavior. This study focuses on managed lane (ML) choice and examines differences in the value of travel time under cumulative prospect theory (CPT) specification versus the EUT. Travelers in our sample are more risk-averse when faced with possibly being late than they are with respect to potential savings in travel time in general. Travelers exhibit optimism (underweight the probability) when the chances of facing a longer travel time are high. The CPT models performed better than traditional models and thus, may prove to be an important tool when considering the benefits of MLs. [ABSTRACT FROM AUTHOR]

We conduct a standardized survey on risk preferences in 53 countries worldwide and estimate cumulative prospect theory parameters from the data. The parameter estimates show that significant differences on the cross-country level are to some extent robust and related to economic and cultural differences. In particular, a closer look on probability weighting underlines gender differences, economic effects, and cultural impact on probability weighting. The data set is a useful starting point for future research that investigates the impact of risk preferences on the market level. [ABSTRACT FROM AUTHOR]

Using a 2012 stated preference survey based on a traveler's most recent actual trip, this study predicts traveler choices between general purpose lanes and managed lanes for a freeway in Houston, Texas. The choice model incorporates probability weighting for risky travel times. The results indicate significant improvement in predicative power over a model that excludes weighting, confirming non-linearity in the probability weighting function. The maximum value of time (VOT) measures calculated in this study are lower than estimated in many previous route choice studies. This highlights the importance of incorporating individual weights for travel risks. Travelers' underweighting of travel time risks would help explain the lower VOTs found in our study because respondents consider route choice decision-making as a gamble, but assign their own probabilities of occurrence to arriving at their destination on time, late, or early. We find that traveler groups are heterogeneous and the different weights developed for different groups of travelers can be used to better understand their probabilities. Segmentation analysis indicates that Age may serve to proxy the effects of more experience over time, or changing driving abilities, or changes in one's sense of optimism or pessimism at different ages. Gender and Income also play a role in how the objective probabilities presented to respondents were translated into subjective probabilities. [ABSTRACT FROM AUTHOR]

Political psychologists have been quick to use prospect theory in their work, realizing its potential for explaining decisions under risk. Applying prospect theory to political decision-making is not without problems, though, and here we address two of these: (1) Does prospect theory actually apply to political decision-makers, or are politicians unlike the rest of us? (2) Which dimension do politicians use as their reference point when there are multiple dimensions (e.g., votes and policy)? We address both problems in an experiment with a unique sample of Dutch members of parliament as participants. We use well-known (incentivized) decision situations and newly developed hypothetical political decision-making scenarios. Our results indicate that politicians' deviate from expected utility theory in the direction predicted by prospect theory but that these deviations are somewhat smaller than those of other people. Votes appear to be a more important determinant of politicians' reference point than is policy. [ABSTRACT FROM AUTHOR]

A number of retailers offer gambling- or lottery-type price promotions with a chance to receive one's entire purchase for free. Although these retailers seem to share the intuition that probabilistic free price promotions are attractive to consumers, it is unclear how they compare to traditional sure price promotions of equal expected monetary value. We compared these two risky and sure price promotions for planned purchases across six experiments in the field and in the laboratory. Together, we found that consumers are not only more likely to purchase a product promoted with a probabilistic free discount over the same product promoted with a sure discount but that they are also likely to purchase more of it. This preference seems to be primarily due to a diminishing sensitivity to the prices. In addition, we find that the zero price effect, transaction cost, and novelty considerations are likely not implicated. This paper was accepted by Yuval Rottenstreich, judgment and decision making. [ABSTRACT FROM AUTHOR]

Multiple price lists have emerged as a simple and popular method for eliciting risk preferences. Despite their popularity, a key downside of multiple price lists has not been widely recognized - namely that the approach is unlikely to generate sufficient information to accurately identify different dimensions of risk preferences. The most popular theories of decision making under risk posit that preferences for risk are driven by a combination of two factors: the curvature of the utility function and the extent to which probabilities are weighted non-linearly. In this paper, we show that the widely used multiple price list introduced by Holt and Laury ( The American Economic Review 92(5) 1644-1655 2002) is likely more accurate at eliciting the shape of the probability weighting function, and we construct a different multiple price list that is likely more accurate at eliciting the shape of the utility function. We show that by combining information from different multiple price lists, greater predictive performance can be achieved. [ABSTRACT FROM AUTHOR]