
on Utility Models and Prospect Theory 
Issue of 2018‒10‒29
sixteen papers chosen by 
By:  Baumgärtner, Stefan; Engler, JohnOliver 
Abstract:  Decisionmaking about economyenvironment systems is often characterized by deep uncertainties. We provide an axiomatic foundation of preferences over lotteries with known payoffs over known states of nature and unknown probabilities of these outcomes (“Knightian uncertainty"). We elaborate the fundamental idea that preferences over Knightian lotteries can be represented by an entropy function (sensu Lieb and Yngvason 1999) of these lotteries. Based on nine axioms on the preference relation and three assumptions on the set of lotteries, we show that there uniquely (up to linearaffine transformations) exists an additive and extensive realvalued function (\entropy function") that represents uncertainty preferences. It represents nonsatiation and (constant) uncertainty aversion. As a concrete functional form, we propose a oneparameter function based on Rényi's (1961) generalized entropy. We show that the parameter captures the degree of uncertainty aversion. We illustrate our preference function with a simple decision problem and relate it to other decision rules under Knightian uncertainty (maximin, maximax, Hurwicz, Laplacian expected utility, minimum regret). 
Keywords:  axiomatic foundation,entropy,Knightian uncertainty,nonexpected utility,preferences,Rényifunction 
JEL:  D81 H30 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:zbw:vfsc18:181511&r=upt 
By:  Simone CerreiaVioglio; Efe A. Ok 
Abstract:  We consider revealed preference relations over risky (or uncertain) prospects, and allow them to be nontransitive and/or fail the classical Independence Axiom. We identify the rational part of any such preference relation as its largest transitive subrelation that satis fies the Independence Axiom and that exhibits some coherence with the original relation. It is shown that this subrelation, which we call the rational core of the given revealed preference, exists in general, and under fairly mild conditions, it is continuous. We obtain various representation theorems for the rational core, and decompose it into other core concepts for preferences. These theoretical results are applied to compute the rational cores of a number of wellknown preference models (such as Fishburns SSB model, justi fiable preferences, and variational and multiplier modes of rationalizable preferences). As for applications, we use the rational core operator to develop a theory of risk aversion for nontransitive nonexpected utility modals (which may not even be complete). Finally, we show that, under a basic monotonicity hypothesis, the Preference Reversal Phenomenon cannot arise from the rational core of ones preferences. JEL Classifi cation: D11, D81. Keywords: Transitive core, affine core, nontransitive nonexpected utility, justi fiable preferences, comparative risk aversion, preference reversal phenomenon. 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:igi:igierp:632&r=upt 
By:  Romain Blanchard; Laurence Carassus (LPMA  Laboratoire de Probabilités et Modèles Aléatoires  UPMC  Université Pierre et Marie Curie  Paris 6  UPD7  Université Paris Diderot  Paris 7  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  This paper formulates an utility indifference pricing model for investors trading in a discrete time financial market under nondominated model uncertainty. The investors preferences are described by strictly increasing concave random functions defined on the positive axis. We prove that under suitable conditions the multiplepriors utility indifference prices of a contingent claim converge to its multiplepriors superreplication price. We also revisit the notion of certainty equivalent for random utility functions and establish its relation with the absolute risk aversion. 
Keywords:  Superreplication price,Knightian uncertainty,multiplepriors,nondominated model,absolute risk aversion,Utility indifference price 
Date:  2018–09–28 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal01883423&r=upt 
By:  Romain Blanchard (LMR  Laboratoire de Mathématiques de Reims  URCA  Université de Reims ChampagneArdenne  CNRS  Centre National de la Recherche Scientifique); Laurence Carassus (Research Center  Léonard de Vinci Pôle Universitaire  De Vinci Research Center, URCA  Université de Reims ChampagneArdenne) 
Abstract:  This paper investigates the problem of maximizing expected terminal utility in a discretetime financial market model with a finite horizon under nondominated model uncertainty. We use a dynamic programming framework together with measurable selection arguments to prove that under mild integrability conditions, an optimal portfolio exists for an unbounded utility function defined on the halfreal line. 
Date:  2018–09–28 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal01883787&r=upt 
By:  Simone CerreiaVioglio; David Dillenberger; Pietro Ortoleva 
Abstract:  One of the most wellknown models of nonexpected utility is Gul (1991)’s bmodel of Disappointment Aversion. This model, however, is defined implicitly, as the solution to a functional equation; its explicit utility representation is unknown, which may limit its applicability. We show that an explicit representation can be easily constructed, using solely the components of the implicit one. We also provide a more general result: an explicit representation for preferences in the Betweenness class that also satisfy Negative Certainty Independence (Dillenberger, 2010). JEL: D80, D81 KEYWORDS: Betweenness, Cautious Expected Utility, Disappointment Aversion, Utility representation. 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:igi:igierp:631&r=upt 
By:  Pierre Gosselin (IF  Institut Fourier  CNRS  Centre National de la Recherche Scientifique  UGA  Université Grenoble Alpes); Aïleen Lotz (Cerca Trova  Université de Lille, Sciences Humaines et Sociales); Marc Wambst (IRMA  Institut de Recherche Mathématique Avancée  UNISTRA  Université de Strasbourg  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  This paper presents an analytical treatment of economic systems with an arbitrary number of agents that keeps track of the systems' interactions and agents' complexity. This formalism does not seek to aggregate agents. It rather replaces the standard optimization approach by a probabilistic description of both the entire system and agents'behaviors. This is done in two distinct steps. A first step considers an interacting system involving an arbitrary number of agents, where each agent's utility function is subject to unpredictable shocks. In such a setting, individual optimization problems need not be resolved. Each agent is described by a timedependent probability distribution centered around his utility optimum. The entire system of agents is thus defined by a composite probability depending on time, agents' interactions and forwardlooking behaviors. This dynamic system is described by a path integral formalism in an abstract spacethe space of the agents' actionsand is very similar to a statistical physics or quantum mechanics system. We show that this description, applied to the space of agents'actions, reduces to the usual optimization results in simple cases. Compared to a standard optimization, such a description markedly eases the treatment of systems with small number of agents. It becomes however useless for a large number of agents. In a second step therefore, we show that for a large number of agents, the previous description is equivalent to a more compact description in terms of field theory. This yields an analytical though approximate treatment of the system. This field theory does not model the aggregation of a microeconomic system in the usual sense. It rather describes an environment of a large number of interacting agents. From this description, various phases or equilibria may be retrieved, along with individual agents' behaviors and their interactions with the environment. For illustrative purposes, this paper studies a Business Cycle model with a large number of agents. 
Keywords:  path integrals,statistical field theory,business cycle,budget constraint,multiagent model,interacting agents 
Date:  2018–10–11 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal01893556&r=upt 
By:  Yasuhiro Sakai (Faculty of Economics, Shiga University) 
Abstract:  This paper aims to focus on the life and work of Daniel Ellsberg, with an intensive discussion on its relation to J.M. Keynes and F.H. Knight, the two great pioneers of the economics of uncertainty. Ellsberg seems to be a man in paradox. When he was young, he was an outstanding researcher at Harvard University and the RAND Corporation; at the December Meting of the Econometric Society in 1960, he presented his remarkable paper in which he successfully demonstrated what we may now call Ellsberg's paradox against the traditional expected theory a la Daniel Bernoulli and von Neumann. Although it was published with the title "Risk, ambiguity and decision" in the November issue of the Quarterly Journal of Economics, it was not paid due attention for a long time. It was partly because he was so preoccupied in the 1960s and onward by letting the general public know the Pentagon papers that he could virtually have no time left to engage in purely academic activities. In the 21st century, however, the times have changed in favor of Ellsberg: we can see the dramatic return of interest in decision making under ambiguity. Chapter ‡U will deal with uncertainties that are not risks. A focal point of discussion will be the similarity and difference between Keynes and Knight. Kenneth Arrow's skepticism about Knight on uncertainty will also be paid due attention. Chapter ‡V, the main part of this paper, will turn to the concept of ambiguity that was first introduced by Ellsberg. The twocolor problem and the three color problem will systematically be examined by help of numerical representations. Chapter ‡W will tell us many alternative ways to solve the socalled Ellsberg paradox. Presumably, the Keynesian approach by means of intervalvalued probabilities will be shown to be very simple and highly effective. In our opinion, the most amazing Ellsberg paradox lies in the fact that an accomplished economist specialized in the aversion of risk and uncertainty dared to make a personal choice to risk everything such as degrading his social status and putting him in prison for a long period. Surely, the intellectual legacy of Ellsberg seems to be an intriguing research in paradox. 
Keywords:  Ellsberg, Keynes, Knight, risk, ambiguity, uncertainty 
JEL:  B21 B22 D81 E12 
Date:  2018–06 
URL:  http://d.repec.org/n?u=RePEc:shg:dpapea:31&r=upt 
By:  Rebeggiani, Luca; Gross, Johannes 
Abstract:  The extent of market efficiency induced by rational behaviour of market participants is central for economic research. Many economists have already examined sportsbetting markets as a laboratory to better understand trading behaviour and efficiency of stock prices while avoiding to jointly test the hypothesis of a correct capital market model. The following paper will investigate whether the European football betting market fulfils the efficiency paradigm introduced by Fama (1970) with a unique dataset allowing for an investigation of the German betting market in view of its regulatory changes recently. The analysis contributes to the literature by conducting a variety of empirical strategy including rational expectation frameworks and an ordered choice model to stress the ex post market performance from a weak and semistrong form perspective. In view of existing market distortions as taxes, switching costs of changing betting providers and limitation in competition, the results of the analysis are indicative of a rational market equilibrium surprisingly close to the efficiency benchmark.1 
Keywords:  Gambling,Sports Betting,Market Efficiency 
JEL:  G14 L83 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:zbw:vfsc18:181563&r=upt 
By:  Giovanni Ponti (Universidad de Alicante, University of Chicago, LUISS Guido Carli Roma); Claudio Rossetti (Università di Napoli Federico II and CSEF) 
Abstract:  In this paper we compare a mixed logit model (MLM) and a latent class model (LCM) in the context of behavioral structural estimation using experimental data. By providing an instrument to deal with the intrinsic unobserved heterogeneity that characterizes experimental data, these alternative models have clear advantages compared with a multinomial logit model (MNL) typically used in structural estimation of behavioral models. We carry out our exercise by using experimental data that allows us estimation of distributional parameters related to risk and social preferences. Somehow coherently with the economic theory, the LCM identifies three classes of subjects (risk/ineq. lovers, risk/ineq. neutral, risk/ineq. averse). Moreover, estimates from both MLM and LCM somehow confirm the findings from a MNL model, that under the veil of ignorance (VOI) subjects’ variance aversion mostly reflects risk, rather than distributional concerns. By taking unobserved heterogeneity adequately into account in the estimation of our structural behavioral model, also provides new insights into individual behavior on the interplay between risk and inequality concerns. For example, we find that there is much more variability in individual behavior when subjects face pure inequality than under VOI. Moreover, in the case of pure inequality subjects are also more likely to be inequality lovers than under VOI. 
Keywords:  Unobserved heterogeneity, Structural behavioral models, Social preferences, Risk preferences. 
JEL:  D86 C25 
Date:  2018–10–18 
URL:  http://d.repec.org/n?u=RePEc:sef:csefwp:512&r=upt 
By:  Vasilev, Aleksandar 
Abstract:  We introduce EpsteinZin (1989, 1991) preferences into a realbusinesscycle setup augmented with a detailed government sector. We calibrate the model to Bulgarian data for the period following the introduction of the currency board arrangement (19992016). We investigate the quantitative importance of the presence of "early resolution of uncertainty" motive for the propagation of cyclical fluctuations in Bulgaria. Allowing for EpsteinZin preferences improves the model performance against data, and in addition this extended setup dominates the standard RBC model framework, e.g., Vasilev (2009). 
Keywords:  business cycle fluctuations,EpsteinZin preferences,Bulgaria 
JEL:  E32 E22 E37 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:zbw:esprep:182577&r=upt 
By:  Tommaso Denti; Massimo Marinacci; Luigi Montrucchio 
Abstract:  In this teaching note we discuss the relation between rational inattention and a major branch of information theory called rate distortion theory. Focusing on methods, we translate tools from rate distortion theory into the language of rational inattention. These tools provide an alternative, more primitive, approach to the study of optimal attention allocation. 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:igi:igierp:630&r=upt 
By:  Romain Blanchard (LMR  Laboratoire de Mathématiques de Reims  URCA  Université de Reims ChampagneArdenne  CNRS  Centre National de la Recherche Scientifique); Laurence Carassus (LPMA  Laboratoire de Probabilités et Modèles Aléatoires  UPMC  Université Pierre et Marie Curie  Paris 6  UPD7  Université Paris Diderot  Paris 7  CNRS  Centre National de la Recherche Scientifique); Miklos Rasonyi 
Abstract:  We consider a discretetime financial market model with finite time horizon and investors with utility functions d efined on the nonnegative halfline. We allow these functions to be random, nonconcave and nonsmooth. We use a dynamic programming framework together with measurable selection arguments to establish both the characterization of the noarbitrage property for such markets and the existence of an optimal portfolio strategy for such investors. 
Keywords:  noarbitrage condition,nonconcave utility functions,optimal investment 
Date:  2018–03–19 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal01883419&r=upt 
By:  Youngju Kim (Economic Research Institute, The Bank of Korea); Hyunjoon Lim (Economic Research Institute, The Bank of Korea) 
Abstract:  We investigate the relative roles of US economic policy uncertainty and global risk aversion in contributing to financial and macroeconomic fluctuations in small open economies (SOEs) using a panel of forty SOEs that includes both advanced economies (AEs) and emerging markets economies (EMEs). We find that SOEs¡¯ financial and real economic activities respond smoothly and persistently to US policy uncertainty shocks, consistent with Bloom et al. (2018), while exhibiting relatively shortlived and robust reactions to US risk aversion shocks. A novel finding of this paper is that the responses of AEs and EMEs are asymmetric: AEs react more strongly to US policy uncertainty shocks while EMEs are more sensitive to risk aversion shocks. These results suggest that the channels through which each shock is transmitted to SOEs may vary. 
Keywords:  Economic Policy Uncertainty, Risk Aversion, Spillovers, Small Open Economies 
JEL:  F21 F32 F42 
Date:  2018–10–02 
URL:  http://d.repec.org/n?u=RePEc:bok:wpaper:1829&r=upt 
By:  Li, Man; Zhang, Wei 
Keywords:  Household and Labor Economics, Risk and Uncertainty, Natural Resource Economics 
Date:  2018–06–20 
URL:  http://d.repec.org/n?u=RePEc:ags:aaea18:274188&r=upt 
By:  Arthur E. Attema (Erasmus School of Economics  Erasmus University Rotterdam, iBMG  Erasmus University Rotterdam); Han Bleichrodt (Erasmus School of Economics  Erasmus University Rotterdam); Olivier L’haridon (CREM  Centre de recherche en économie et management  UNICAEN  Université de Caen Normandie  NU  Normandie Université  UR1  Université de Rennes 1  UNIVRENNES  Université de Rennes  CNRS  Centre National de la Recherche Scientifique); Patrick PerettiWatel (SESSTIM  U1252 INSERM  AMU  UMR 259 IRD  Sciences Economiques et Sociales de la Santé & Traitement de l'Information Médicale  IRD  Institut de Recherche pour le Développement  AMU  Aix Marseille Université  INSERM  Institut National de la Santé et de la Recherche Médicale); Valérie Seror (SESSTIM  U1252 INSERM  AMU  UMR 259 IRD  Sciences Economiques et Sociales de la Santé & Traitement de l'Information Médicale  IRD  Institut de Recherche pour le Développement  AMU  Aix Marseille Université  INSERM  Institut National de la Santé et de la Recherche Médicale) 
Abstract:  This study compares discounting for money and health in a field study. We applied the direct method, which measures discounting independent of utility, in a representative French sample, interviewed at home by professional interviewers. We found more discounting for money than for health. The median discount rates (6.5% for money and 2.2 % for health) were close to market interest rates suggesting that the direct method solves the puzzle of unrealistically high discount rates typically observed in applied economics. Constant discounting fitted the data better than hyperbolic discounting. The substantial individual heterogeneity in discounting could be explained by age and occupation. 
Keywords:  Hyperbolic discounting,Constant discounting,Health versus money,Time preference,Direct method,Field study 
Date:  2018–05–09 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:halshs01683771&r=upt 
By:  Bruhin, Adrian (University of Lausanne); Fehr, Ernst (University of Zurich); Schunk, Daniel (University of Mainz) 
Abstract:  There is vast heterogeneity in the human willingness to weigh others' interests in decision making. This heterogeneity concerns the motivational intricacies as well as the strength of otherregarding behaviors, and raises the question how one can parsimoniously model and characterize heterogeneity across several dimensions of social preferences while still being able to predict behavior over time and across situations. We tackle this task with an experiment and a structural model of preferences that allows us to simultaneously estimate outcomebased and reciprocitybased social preferences. We find that nonselfish preferences are the rule rather than the exception. Neither at the level of the representative agent nor when we allow for several preference types do purely selfish types emerge in our sample. Instead, three temporally stable and qualitatively different otherregarding types emerge endogenously, i.e., without prespecifying assumptions about the characteristics of types. When ahead, all three types value others' payoffs significantly more than when behind. The first type, which we denote as strongly altruistic type, is characterized by a relatively large weight on others' payoffs – even when behind – and moderate levels of reciprocity. The second type, denoted as moderately altruistic type, also puts positive weight on others' payoff, yet at a considerable lower level, and displays no positive reciprocity, while the third type is behindness averse, i.e., puts a large negative weight on others' payoffs when behind and behaves selfishly otherwise. We also find that there is an unambiguous and temporally stable assignment of individuals to types. In addition, we show that individualspecific estimates of preferences offer only very modest improvements in outofsample predictions compared to our threetype model. Thus, a parsimonious model with only three types captures the bulk of the information about subjects' social preferences. 
Keywords:  social preferences, heterogeneity, stability, finite mixture models 
JEL:  C49 C91 D03 
Date:  2018–09 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp11815&r=upt 