Non-expected Utility Models Research Articles

Recursive two-stage evaluation model for dynamic decision making under ambiguity

In this paper, the two-stage-evaluation (TSE) model for decision making under ambiguity (He 2021) is extended to intertemporal setting in an axiomatic approach. The first set of axioms employed are commonly adopted for dynamic non-expected utility models in the literature. Besides these regular axioms, I also assume dynamic consistency and conditions which deliver a static TSE for consumption plans only pay non-zero consequences for one period. It is shown that these axioms hold if and only if these exists a recursively defined evaluation utility model representing decision maker (DM)’s preferences over consumption plans conditional on arriving at any node in an event tree. Such a recursive form implies that one can apply dynamic programming technique (rolling back the decision tree) to solve a dynamic decision making problem under TSE model. It can be shown that the solution for the recursively defined dynamic TSE model exists uniquely. Due to the “small domain” setup, the agent is short-sighted in the sense that they only process subjective probabilities over events defined on one period uncertainty over next period states, which differs from “far-sighted” assumption in most extant models that assume subjective probabilities exist over events defined on multiple periods. It is shown that under some extra conditions, our DM applies Bayes’ rule “updating’ her subjective beliefs.

Optimal allocations with α‐MaxMin utilities, Choquet expected utilities, and prospect theory

The analysis of optimal risk sharing has been thus far largely restricted to nonexpected utility models with concave utility functions, where concavity is an expression of ambiguity aversion and/or risk aversion. This paper extends the analysis to α‐maxmin expected utility, Choquet expected utility, and cumulative prospect theory, which accommodate ambiguity seeking and risk seeking attitudes. We introduce a novel methodology of quasidifferential calculus of Demyanov and Rubinov (1986, 1992) and argue that it is particularly well suited for the analysis of these three classes of utility functions, which are neither concave nor differentiable. We provide characterizations of quasidifferentials of these utility functions, derive first‐order conditions for Pareto optimal allocations under uncertainty, and analyze implications of these conditions for risk sharing with and without aggregate risk.

Behavioral Theories That Have Influenced the Way Health State Preferences Are Elicited and Interpreted: A Bibliometric Mapping Analysis of the Time Trade-Off Method With VOSviewer Visualization.

The aim of this paper is to develop an understanding of how behavioral theories have influenced the way preferences for health-related quality of life are elicited and interpreted. We focus on the Time Trade-off (TTO) method given it represents the quality-adjusted life-year (QALY) concept-that survival in less-than-full health can be deemed equivalent to a shorter survival in full health. To our knowledge this is the first review using a combination of systematic scoping review, bibliometrics and VOSviewer visualization to map the development of ideas in health economics. A priori, we selected three behavioral theories to explore within our review, referred to here as Expected Utility Theory, Non-Expected Utility Theory and Probabilistic Choice Theory. A fourth topic, Order Effects, is defined broadly to encompass behavioral theories around timing/sequence of events. For the main search, Scopus was used to identify literature that had (a) elicited TTO values and/or (b) contributed to the way TTO values were elicited and interpreted, from inception to July 2021. Papers that focused on the latter category were given the label "behavioral" and underwent additional analyses. A two stage-screening was applied to assess eligibility. Co-citation, co-authorship and co-occurrence of keywords was used to chart the development of TTO over time. A total of 1,727 records were retrieved from Scopus and were supplemented by an additional 188 papers. There were 856 applied and 280 behavioral papers included in the final corpus, with the behavioral set split equally into four sets of 70 papers to chart the development of keywords over time: (1) 1972-1999; (2) 2000-2010, (3) 2010-2015 and (4) 2015-2021. The keyword analysis suggested that whilst some ideas transition quickly from economic theory to the TTO literature, such as the impact of Order Effects, others take longer to be assimilated, for example Non-Expected Utility models or failure of constant discounting. It is therefore important that researchers within health economics work more closely with those in mainstream economics and keep abreast of the wider economics and behavioral sciences to expedite the uptake of new and relevant ideas.

A non-expected utility model and its application in practical auctions

ABSTRACT This article presents a non-expected utility decision model which is nonlinear in the winning probabilities. The model not only explicitly expresses bidders’ attitudes to risk, but also addresses their preference over the bidding criteria. To demonstrate how to apply the model in the practical auction design, the first- and second-price auctions with both commission rate and reserve price are examined, respectively. For nonrisk-neutral bidders, the equilibrium bidding strategies are characterized, in which the commission rate has a significant influence on the bidding strategy through the critical valuation. However, the existence of the optimal commission rate is uncertain, but once it exists, it depends on the information rent of the highest or second highest order valuation in terms of the inverse hazard rate. With risk-aversion bidders, the only difference to the optimal reserve price is a constant between the first- and second-price auctions. The revenue comparisons show that the classical Revenue Equivalence Theorem fails in practical auctions with the commission rate. This article extends the application of the decision-making model in the auction design in theory and provides some guidance for the auction house and the seller to make their decisions in reality.

On the consensus effect

Individuals often tend to conform to the choices of others in group decisions, compared to choices made in isolation. We show that this behavior — which we term the consensus effect — is equivalent to a well-known violation of expected utility, namely strict quasi-convexity of preferences, which is shared by many popular non-expected utility models. In contrast to the equilibrium outcome when individuals are expected utility maximizers, quasi-convexity of preferences imply that group decisions may fail to properly aggregate preferences and strictly Pareto-dominated equilibria may arise.

Optimal Insurance Level Without the Expected-Utility Framework

Mossin's Theorem (full insurance with a fair premium and partial insurance with an unfair premium) is re-examined without the expected-utility paradigm where risk-aversion is defined in terms of mean-preserving spreads. Under the same assumption, two key results are known to hold for coinsurance: (1) Mossin's Theorem needs to be modified, and (2) the culprit for invalidating Mossin's Theorem is not the lack of an expected-utility framework, but a lack of sufficient ``smoothness'' of preferences in non-expected utility models. This article establishes that the first result holds for any constrained class of insurance contracts, and that the second result is not valid for deductible insurance and upper-limit insurance.

Recursive non-expected utility: Connecting ambiguity attitudes to risk preferences and the level of ambiguity

I study how risk preferences and the level of ambiguity influence ambiguity attitudes in Uzi Segal's recursive second-order non-expected utility model. It is shown that the negative certainty independence axiom for risk preferences is equivalent to a global form of ambiguity aversion that entails ambiguity averse behavior irrespective of the state space and the decision maker's second-order belief. Thus, the second-order version of the cautious expected utility model is the only subclass of Segal's theory that robustly predicts ambiguity aversion. Moreover, a mean-preserving spread operation over second-order beliefs, which corresponds to a particular way of increasing the level of ambiguity, is equivalent to increasing the relative strength of ambiguity aversion for each possible specification of risk preferences within the cautious expected utility model. An application of the latter result establishes a negative relation between participation rates in an asset market and the level of ambiguity concerning the distribution of returns.

Access-Based Beliefs: Do individuals experience sour grapes over unattainable alternatives?

Access-based beliefs are the notion that the probability of obtaining an alternative in a choice set may directly impact beliefs about its value. Individuals may make themselves feel better by lowering beliefs of alternatives to which they have limited access; conversely, individuals may find inaccessible alternatives more appealing and increase beliefs of their value. We interpret the first sensation as sour grapes and the second as the grass-is-greener. In a controlled lab experiment that precludes learning, we examine how the probability of obtaining a binary ambiguous prospect influences beliefs. We find that a 60 p.p. reduction in access decreases beliefs of the likelihood of a high contingent payout by 3 p.p. (.2 standard deviations) amongst subjects with coherent beliefs, thus showing that the sour grapes channel outweighs the grass-is-greener in a context that resembles real economic decisions, and demonstrating a novel violation of subjective expected utility. We use a Brunnermeier and Parker optimal beliefs model with an additional source of psychological utility, loss-aversion, to explain access-based beliefs and rule out prominent non-expected utility models as being able to explain our results. We discuss how sour grapes can lead to a belief-based poverty trap and present results of our experiment from India that show a stronger sour grapes effect.

The Simplest Non-Expected Utility Model for Lottery and Portfolio Choices

Abstract This paper explores a particularly simple model of choice under risk, based on geometric means and entropy. Despite its simplicity, it satisfies various prudence and risk aversion conditions, is consistent with the Allais paradox, and generates various insurance-related results. Within a portfolio framework with compounded reinvestments, our index fits the risks/rewards data from post-war US stock market returns and recent international markets, at least as well as does the standard deviation measures more typically used. It also generates returns that are consistent with the equity premium puzzle.

Testing ambiguity and Machina preferences within a quantum-theoretic framework for decision-making

The Machina thought experiments pose to major non-expected utility models challenges that are similar to those posed by the Ellsberg thought experiments to subjective expected utility theory (SEUT). We test human choices in the ‘Ellsberg three-color example’, confirming typical ambiguity aversion patterns, and the ‘Machina 50/51 and reflection examples’, partially confirming the preferences hypothesized by Machina. Then, we show that a quantum-theoretic framework for decision-making under uncertainty recently elaborated by some of us allows faithful modeling of the collected data. In the quantum-theoretic framework, subjective probabilities are represented by quantum probabilities, while quantum state transformations enable representations of ambiguity aversion and subjective attitudes toward it.

Information and Ambiguity: Toward a Foundation of Nonexpected Utility

The concept of ambiguity designates those situations where the information available to the decision maker is insufficient to form a probabilistic view of the world. Thus, it has provided the motivation for departing from the subjective expected utility (SEU) paradigm. Yet, the formalization of the concept is missing. This is a grave omission as it leaves nonexpected utility models hanging on shaky ground. In particular, it leaves unanswered basic questions such as the following: (1) Does ambiguity exist? (2) If so, which situations should be labeled as “ambiguous”? (3) Why should one depart from SEU in the presence of ambiguity? (4) If so, what kind of behavior should emerge in the presence of ambiguity? The present paper fills these gaps. Specifically, it identifies those information structures that are incompatible with SEU theory, and shows that their mathematical properties are the formal counterpart of the intuitive idea of insufficient information. These are used to give a formal definition of ambiguity and, consequently, to distinguish between ambiguous and unambiguous situations. Finally, the paper shows that behavior not conforming to SEU theory must emerge in correspondence of insufficient information and identifies the class of non-EU models that emerge in the face of ambiguity. The paper also proposes a new comparative definition of ambiguity, and discusses its relation with some of the existing literature.

Cautious and Globally Ambiguity Averse

I study ambiguity attitudes in Uzi Segal's recursive non-expected utility model. I show that according to this model, the negative certainty independence axiom over simple lotteries is equivalent to a robust, or global form of ambiguity aversion that requires ambiguity averse behavior irrespective of the number of states and the decision maker's second-order belief. Thus, the recursive cautious expected utility model is the only subclass of Segal's model that robustly predicts ambiguity aversion. Similarly, the independence axiom over lotteries is equivalent to a robust form of ambiguity neutrality. In fact, any non-expected utility preference over lotteries coupled with a suitable second-order belief over three states produces either the Ellsberg paradox or the opposite mode of behavior. Finally, I propose a definition of a mean-preserving spread for second-order beliefs that is equivalent to increasing ambiguity aversion for every recursive preference that satisfies the negative certainty independence axiom.

Impact of Non Professional Physicians' Characteristics on Medical Decision Making in Older Patients with Acute Myeloid Leukemia

Frontline therapy for newly diagnosed AML in older adults can be classified as "more" or "less" intensive. Assignment of patients (pts) to intensive chemotherapy (ICT) or low-intensity therapy (LIT) such as hypomethylating agents (HMA), low-dose aracytine (LDAC) or best supportive care (BSC), should be based on patient- and disease-related prognosis factors. Although scoring systems have been proposed to rationalize this clinical decision-making, there is a strong heterogeneity in clinical practice. Cancer management study mainly focused on patients' determinants of care but very few have assessed the influence of physicians' characteristics and none in AML. In behavioral sciences, attitudes towards risk and ambiguity are psychological traits that may explain medical choices. These traits are connected with theoretical models of decision under uncertainty that can be divided in Expected Utility (EU) and Non-Expected Utility (Non-EU) models where the former is often considered as a benchmark of "economic rationality". Choice patterns in decision task known as Allais paradox allow classifying individuals in these two classes of models. In addition, behavioral consequences when the probabilities of uncertain events are unknown are defined as ambiguity attitudes.Our study investigated the impact of physician's characteristics on their medical decisions regarding 6 clinical vignettes of older AML pts that highlight distinct and difficult situations derived from clinical practice.Physicians’ demographical and occupational characteristics were collected through a national cross-sectional web survey among French hematologists. We categorized physicians as EU or non-EU using their responses to the binary lottery choice questions of the Allais paradox (Kahneman & Tversky, 1979). A last question elicited a certainty equivalent (sure gain between 0 and 500 euros) of an ambiguous lottery (Abdellaoui & al, 2011) as a proxy of physicians’ ambiguity tolerance.Physicians were asked to decide how to treat (ICT, LIT or BSC) elderly AML pts presented in 6 vignettes (table1). Assessable respondents included those who answered all cases. We used k-means clustering method in order to define clinician's groups with homogeneous pattern of responses to the clinical cases.Among the 230 physicians with assessable answers, the median age was 42 years [standard deviation (SD)± 11.2], 123 were male (54%), 160 were consultant or professor (70%), 166 worked in an academic center (72%), 197 were specialized in hematology (86%), and the mean number of older AML pts treated a year per physician was 20.7 (SD ± 17.1). Regarding the Allais paradox, EU, non-EU and undefined represented respectively 101 (43.9%), 109 (47.3%) and 20 (8.7%) respondents. Regarding ambiguity tolerance, the mean of the certainty equivalent was 241 euros (SD ±136).From the pattern of responses to the vignettes, the K-means clustering yielded two distinct groups identified as (1) clinicians who were more prone to prescribe "more" intensive therapy (ICT), and (2) clinicians who were more prone to prescribe "less" intensive therapy (LIT or BSC).We studied the factors associated with the probability of belonging to the "more intensive" category of physicians. A multivariate model (n=210) on variables identified from the bivariate analyses systematically adjusted for age and gender highlighted the following effects and trend:ambiguity tolerant physicians prescribe significantly less ICT (OR 0.87 [for each 50 euros-increase]; 95%CI, 0.77-0.99, p=0.039), physicians not conforming to expected utility ("economically irrational") recommend more ICT (OR 1.85; 95%CI, 0.92-3.73, p=0.084) and female physicians tend to prescribe less ICT (OR 0.58; 95%CI, 0.28-1.20, p=0.14).Physicians' age, hierarchical status, hospital facility or volume of older AML pts treated a year were not associated with the clusters.Final results of national cross-sectional study performed on French hematologists, show that physicians' attitudes towards risk and ambiguity, i.e. physicians' nonprofessional characteristics, may influence their medical decision making process between "more" and "less" intensive therapy for older AML patients. The extension of this study in different countries is planned to test the cross-cultural robustness of our results and increase our knowledge on psychological traits that could influence physicians' practice. [Display omitted] [Display omitted] DisclosuresMalak:Novartis: Membership on an entity's Board of Directors or advisory committees. Recher:Celgene, Sunesis, Amgen, Novartis, Chugai: Research Funding; Celgene, Sunesis, Amgen, Novartis: Membership on an entity's Board of Directors or advisory committees.

Inference under stability of risk preferences

We leverage the assumption that preferences are stable across contexts to partially identify and conduct inference on the parameters of a structural model of risky choice. Working with data on households' deductible choices across three lines of insurance coverage and a model that nests expected utility theory plus a range of non-expected utility models, we perform a revealed preference analysis that yields household-specific bounds on the model parameters. We then impose stability and other structural assumptions to tighten the bounds, and we explore what we can learn about households' risk preferences from the intervals defined by the bounds. We further utilize the intervals to (i) classify households into preference types and (ii) recover the single parameterization of the model that best fits the data. Our approach does not entail making distributional assumptions about unobserved heterogeneity in preferences.

Incomplete preferences and confidence

A theory of incomplete preferences under uncertainty is proposed, according to which a decision maker’s preferences are indeterminate if and only if her confidence in the relevant beliefs does not match up to the stakes involved in the decision. We use the representation of confidence in beliefs introduced in Hill (2013), and axiomatise a class of models, differing from each other in the appropriate notion of stakes. The theory naturally suggests two distinct strategies for completing preferences, and hence for choosing in the presence of incompleteness: one that relies only on beliefs in which the decision maker is sufficiently confident, and one that mobilises all beliefs, no matter how little confidence she may have in them. Axiomatic characterisations are given for completion procedures following each of the strategies. Finally, in a market setting, the incorporation of confidence is shown to add an extra friction, beyond the standard implications of non-expected utility models for Pareto optima.

Timing the stock market: Does it really make no sense?

Many private and institutional investors attempt to time the market and generate abnormal returns by periodically switching their portfolio allocations between the stock market and the cash market based on their return predictions. However, most academic studies emphasize that a successful market timing strategy requires a prediction accuracy that is usually not observable in reality. While prior studies evaluate the outcomes based on traditional return and risk measures, we adopt both expected and non-expected utility models to compare market timing with common benchmarks. Our analyses are based on a “simulated market timer” that does not require a specific forecast model. Bootstrap-based simulations show that even with low hit ratios, investors with non-expected utility preferences can consider market timing as highly desirable. The attractiveness of market timing is also partly attributable to short-termism in performance evaluation.

Comment on Halevy (2007) 'Ellsberg Revisited: An Experimental Study'

Halevy (2007) experimentally tests the prediction of the Recursive Non-Expected Utility (RNEU) model that there is a positive correlation between degree of ambiguity aversion and degree of preference on reduction of compound lotteries ROCL. Halevy (2007) claimed that the experimental result supports the RNEU. In this study, we use Halevy’s data and conduct further analysis based on subject’s ambiguity attitude types: ambiguity neutral, ambiguity averse, and ambiguity loving. We find striking different results. First, there is no significant relationship between degree of preference on ROCL and degree of ambiguity aversion. Second, subjects who prefer simple lotteries are not more likely to be ambiguity averse than subjects who prefer compound lotteries. Third, ambiguity averse subjects are not more likely to prefer simple lottery than those who are ambiguity seeking. In sum, there is no evidence that ambiguity aversion can be well explained by preference on reduction of compound lotteries.

The optimal hedge for carbon market: an empirical analysis of EU ETS

The paper uses non-expected utility model and hedging cost model to analyse carbon market. The results show that investors prefer to hold spot goods in carbon market in 2008-2012 than in 2005-2007. Hedging ratio is about 0.1 and 0.4 in 2005-2007 and 2008-2012 respectively for the international politics and negotiations leads to great volatility and complex changes in the carbon price, the optimal hedging ratio in carbon market is lower than general market. When disappointment aversion and risk aversion coefficient is extremely high or extremely low, deviations can be easily generated during carbon market judgment. The simulation indicates that returns sequences of future goods and spot goods in carbon market have no linear dependence. At present, future market cannot well provide hedging function for spot market.

RECURSIVE AMBIGUITY AND MACHINA'S EXAMPLES

Machina (American Economic Review 99 (2009), 385–392; American Economic Review 104 (2014), 3814–40) lists a number of situations where Choquet expected utility, as well as other known models of ambiguity aversion, cannot capture plausible features of ambiguity attitudes. Most of these problems arise in choice over prospects involving three or more outcomes. We show that the recursive nonexpected utility model of Segal (International Economic Review 28 (1987), 175–202) is rich enough to accommodate all these situations and, moreover, that this can be done using the same functional form for all situations.

Aversion to Risk and Downside Risk in the Large and in the Small under Non-Expected Utility: A Quantile Approach

This paper proposes a decomposition of the cost of risk (as measured by a risk premium) across intervals/quantiles of the payoff distribution. The analysis is based on general smooth risk preferences. While this includes the expected utility model as a special case, the investigation is done under a broad class of non-expected utility models. We decompose the risk premium into additive components across quantiles. Defining downside risk as the risk associated with a lower quantile, this provides a basis to evaluate the cost of exposure to downside risk. We derive a local measure of the cost of risk associated with each quantile. It establishes linkages between the cost of risk, risk preferences and the distribution of risky prospects across quantiles (as measured by quantile variance and skewness). The analysis gives new and useful information on how risk aversion, exposure to downside risk and departures from the expected utility model interact as they affect the risk premium.