
on Utility Models and Prospect Theory 
By:  Moez Abouda (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, BESTMOD  Institut Supérieur de Gestion de Tunis) 
Abstract:  La Vallée (1968), in the expected utility model, gives a sufficient condition for positivity of the bidselling spread. In this article, we show that this sufficient condition, namely decreasing absolute risk aversion (DARA) is in fact necessary. Moreover, we prove that the expected utility hypothesis and differentiability of the utility function are not required. 
Keywords:  DARA, NARA, bidselling spread, perfect hedging, risk premium. 
Date:  2008–03 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00270648_v1&r=upt 
By:  Thibault Gajdos (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris); Takashi Hayashi (Department of Economics, University of Texas at Austin  University of Texas at Austin); JeanMarc Tallon (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris); JeanChristophe Vergnaud (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris) 
Abstract:  This paper presents an axiomatic model of decision making under uncertainty which incorporates objective but imprecise information. Information is assumed to take the form of a probabilitypossibility set, that is, a set $P$ of probability measures on the state space. The decision maker is told that the true probability law lies in $P$ and is assumed to rank pairs of the form $(P,f) $ where $f$ is an act mapping states into outcomes. Thekey representation result delivers maxmin expected utility where the min operator ranges over a set of probability priors just as in the maxmin expected utility (MEU) representation result of \cite{GILB/SCHM/89}. However, unlike the MEU representation, the representation here also delivers a mapping, $\varphi$, which links the probabilitypossibility set, describing the availableinformation, to the set of revealed priors. The mapping $\varphi$ is shown to represent the decision maker's attitude to imprecise information: under our axioms, the set of representation priors is constituted as a selection from the probabilitypossibility set.This allows both expected utility when the selected set is a singleton and extreme pessimism when the selected set is the same as the probabilitypossibility set, i.e. , $\varphi$ is the identity mapping. We define a notion of comparative imprecision aversion and show it is characterized by inclusion of the sets of revealedprobability distributions, irrespective of the utility functions that capture risk attitude. We also identify an explicit attitude toward imprecision that underlies usual hedging axioms. Finally, we characterize, under extra axioms, a more specific functional form, in which the set of selected probability distributions is obtained by (i) solving for the ``mean value'' of the probabilitypossibility set, and (ii) shrinking the probabilitypossibility set toward the mean value to a degree determined by preferences. 
Keywords:  precise information, imprecision aversion, multiple priors, Steiner point. 
Date:  2008–05 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00177378_v1&r=upt 
By:  Claudio Campanale (Universidad de Alicante); Gian Luca Clementi (New York University); Rui Castro (Université de Montréal) 
Abstract:  In this paper we provide a thorough characterization of the asset returns implied by a simple general equilibrium production economy with convex investment adjustment costs. When households have EpsteinZin preferences, there exist plausible parametervalues such that the model generates unconditional mean riskfree rate and equity return, and volatility of consumption growth, which are in line with historical averages for the US economy. Consistently with the data, the model's implied pricedividendratio is procyclical and stock returns are predictable (and increasingly so as the time horizon increases), while dividend growth is not. The model also implies realistic values for (i) the correlation of the riskfree rate with output growth and consumption growth and (ii) the correlation pattern between riskfree rate, equity return, and equity premium. The risk implied by the model is rather low. At the modal state of nature, an individual that expects to consume for 100,000 dollars a year faces a lottery over future consumption with a standard deviation of 55 dollars (per quarter). Her risk aversion is such that she's willing to pay 1 dollar (per quarter) in order to avoid that lottery. Very similar results can be obtained assuming that agents are disappointment averse in the sense of Gul (1991). With such risk preferences, the universality requirement is not a problem to the extent that it is in the case of expected utility. In fact, faced with a lottery that has a coefficient of variation 100 times as large as that implied by our model, a disappointment averse agent displays the same relative risk aversion as an expected utility agent with logarithmic utility! 
Keywords:  Equity Premium, Business Cycle, Predictability, Disappointment Aversion. 
JEL:  D81 E32 E43 E44 G12 
Date:  2008–10 
URL:  http://d.repec.org/n?u=RePEc:ivi:wpasad:200814&r=upt 
By:  Sophie Jallais (PHARE  Pôle d'Histoire de l'Analyse et des Représentations Economiques  CNRS : FRE2541  Université PanthéonSorbonne  Paris I  Université de Paris X  Nanterre); PierreCharles Pradier (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, SAMOS  Statistique Appliquée et MOdélisation Stochastique  Université PanthéonSorbonne  Paris I); David Teira (Dpto. de Lógica, Historia y Filosofía de la ciencia. UNED  uned) 
Abstract:  In this paper we want to explore an argumentative pattern that provides a normative justification for expected utility functions grounded on empirical evidence, showing how it worked in three different episodes of their development. The argument claims that we should prudentially maximize our expected utility since this is the criterion effectively applied by those who are considered wisest in making risky choices (be it gamblers or businessmen). Yet, to justify the adoption of this rule, it should be proven that this is empirically true: i.e., that a given function allows us to predict the choices of that particular class of agents. We show how expected utility functions were introduced and contested in accordance to this pattern in the 18th century and how it recurred in the 1950s when M. Allais made his case against the neobernoullians. 
Keywords:  Expected utility;Normative theory; 
Date:  2008–05 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00274361_v1&r=upt 
By:  De Langhe, B.; Sweldens, S.T.; Osselaer, S.M.J. van; Tuk, M.A. (Erasmus Research Institute of Management (ERIM), RSM Erasmus University) 
Abstract:  Two experiments show that a shortage of selfregulatory resources results in more risk aversion in mixedgamble (gain/loss) situations. The findings support a dual process view that distinguishes between a rational and an affective information processing system, in which selfregulatory resources are the necessary fuel for the rational system. Depending on the expected values of risk seeking versus risk averse behavior, ego depletion can have negative (experiment 1) as well as positive (experiment 2) consequences for investment behavior. 
Keywords:  emotional information processing system;risk averse;ego depletion;investment behavior 
Date:  2008–10–20 
URL:  http://d.repec.org/n?u=RePEc:dgr:eureri:1765013614&r=upt 
By:  RoseAnne Dana (CEREMADE  CEntre de REcherches en MAthématiques de la DEcision  CNRS : UMR7534  Université Paris Dauphine  Paris IX); Cuong Le Van (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris) 
Abstract:  The theory of existence of equilibrium with shortselling is reconsidered under risk and ambiguity modelled by risk averse variational preferences. A sufficient condition for existence of efficient allocations is that the relative interiors of the risk adjusted sets of expectations overlap. This condition is necessary if agents are not risk neutral at extreme levels of wealths either positive or negative. It is equivalent to the condition that there does not exist mutually compatible trades, with non negative expected value with respect to any risk adjusted prior, strictly positive for some agent and some prior. It is shown that the more uncertainty averse and the more risk averse, the more likely are efficient allocations and equilibria to exist. 
Keywords:  Uncertainty, risk, common prior, equilibria with shortselling, variational preferences. 
Date:  2008–05 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00281582_v1&r=upt 
By:  Alain Chateauneuf (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I); Michel Grabisch (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I); Agnès Rico (LIRIS  Laboratoire d'Informatique en Images et Systèmes d'Information  CNRS : UMR5205  Université Claude Bernard  Lyon I  Université Lumière  Lyon II  Institut National des Sciences Appliquées de Lyon  Ecole Centrale de Lyon) 
Abstract:  The aim of the paper is to present under uncertainty, and in an ordinal framework, an axiomatic treatment of the Sugeno integral in terms of preferences which parallels some earlier derivations devoted to the Choquet integral. Some emphasis is given to the characterization of uncertainty aversion. 
Keywords:  Sugeno integral; uncertainty aversion; preference relations; ordinal information 
Date:  2008 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00327700_v1&r=upt 
By:  Michèle Cohen (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I); Johanna Etner (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, LIRAES  Université Paris Descartes  Paris V); Meglena Jeleva (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, GAINS  Université du Maine) 
Abstract:  The aim of the paper is to propose a preferences representation model under risk where risk perception can be past experience dependent. A first step consists in considering a one period decision problem where individual preferences are no more defined only on decisions but on pairs (decision, past experience). The obtained criterion is used in the construction of a dynamic choice model under risk. The paper ends with an illustrative example concerning insurance demand. Itappears that our model allows to explain modifications in the insurance demand behavior over time observed on the insurance markets for catastrophic risk and difficult to justify with standard models. 
Keywords:  dynamic decision making  past experience  rank dependent utility model  recursive model  risk perception 
Date:  2008–03 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00211942_v1&r=upt 
By:  Jan Heufer 
Abstract:  Revealed Preference offers nonparametric tests for whether consumption observations can be rationalized by a utility function. If a consumer is inconsistent with GARP, we might need a measure for the severity of inconsistency. One widely used measure is the Afriat efficiency index (AEI).We propose a new measure based on the extent to which the indifference surfaces intersect the budget hyperplanes. The measure is intuitively appealing and, as a cutoff rule evaluated by Monte Carlo experiments, performs very well compared to the AEI. The results suggest that the new measure is better suited to capture small deviations from utility maximation. 
Keywords:  Consumer choice, efficiency index,GARP, nonparametric tests, revealed preference 
JEL:  C14 C60 D11 D12 
Date:  2008–09 
URL:  http://d.repec.org/n?u=RePEc:rwi:repape:0069&r=upt 
By:  Alain Ayong Le Kama (EQUIPPE  Université de Lille I); Cuong Le Van (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris); Katheline Schubert (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris) 
Abstract:  There are two main approaches for defining social welfare relations for an economy with infinite horizon. The first one is to consider the set of intertemporal utility streams generated by a general set of bounded consumptions and define a preference relation between them. This relation is ideally required to satisfy two main axioms, the Pareto axiom, which guarantees efficiency and the Anonymity axiom, which guarantees equity. Basu and Mitra (2003) show that it is impossible to represent by a function a preference relation embodying both requirements, and Basu and Mitra (2007) propose and characterize a new welfare criterion called utilitarian social welfare relation. In the same framework, Chichilnisky (1996) proposes two axioms that capture the idea of sustainable growth : nondictatorship of the present and nondictatorship of the future, and exhibits a mixed criterion, adding a discounted utilitarian part, which gives a dictatorial role to the present, and a long term part, which gives a dictatorial role to the future. The drawback of Chichilnisky's approach is that it often does not allow to explicity characterize optimal growth paths with optimal control techniques. Our aim is less general than Chichilnisky's and Basu and Mitra's : we want to have a nondictatorial criterion for optimal growth models. We restrict ourselves to the set of utilities of consumptions which are generated by a specific technology. We show that the undiscounted utilitarian criterion pioneered by Ramsey (1928) is not only convenient if one wants to solve an optimal growth problem but also sustainable, efficient and equitable. 
Keywords:  Anonymity, intergenerational equity, natural resources, nondictatorship of the future, nondictatorship of the present, optimal growth models, Pareto, social welfare function, social welfare relation, sustainability, utilitarian undiscounted criterion. 
Date:  2008–04 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00275758_v1&r=upt 
By:  Julio Davila (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris) 
Abstract:  I establish, in simple deterministic overlapping generations economies, that if each agent holds rationally formed expectations in the sense that any other expectations justifying his choices imply a smaller likelihood for the history he observes with limited memory, then there are rationally formed expectations equilibria exhibiting an excess volatility that no rational expectations equilibrium can match. Given that the limited records or finite memory case may arguably be the relevant one from a positive viewpoint, this result suggests that the possibility of excess volatility as an equilibrium phenomenon has been downplayed by the use of the rational expectations hypothesis. 
Keywords:  Expectations, rationality, volatility. 
Date:  2008–02 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00261582_v1&r=upt 
By:  Thibault Gajdos (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I); JeanMarc Tallon (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I); JeanChristophe Vergnaud (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I) 
Abstract:  We axiomatize in the Anscombe–Aumann setting a wide class of preferences called rankdependent additive preferences that includes most known models of decision under uncertainty as well as state dependent versions of these models. We prove that aggregation is possible and necessarily linear if and only if (society's) preferences are uncertainty neutral. The latter means that society cannot have a nonneutral attitude toward uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate multiple prior agents, even when they all have the same set of priors. A number of ways to restore the possibility of aggregation are then discussed. 
Keywords:  Aggregation; Uncertainty 
Date:  2008 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00266049_v1&r=upt 
By:  Youichiro Higashi (Department of economics  University of Rochester); Sujoy Mukerji (Oxford University  University of Oxford); Norio Takeoka (Department of economics  University of Rochester); JeanMarc Tallon (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris) 
Abstract:  The final step in the proof of Proposition 1 (p.311) of Mukerji and Tallon (2003) may not hold in generalbecause $\varepsilon>0$ in the proof cannot be chosen independently of $w,z$. We point out by a counterexample that the axioms they impose are too weak for Proposition 1. We introduce a modified set of axioms and reestablish theproposition 
Keywords:  ambiguity;bid ask spread;Ellsberg paradox 
Date:  2008 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00175266_v1&r=upt 
By:  MarcArthur Diaye (CEE  Centre d'Etudes de l'Emploi  Ministère de la recherche  Ministère chargé de l'Emploi, EPEE  centre d'Etudes des Politiques Economiques de l'université d'Evry  Université d'EvryVal d'Essonne); François Gardes (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I); Christophe Starzec (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I) 
Abstract:  The purpose of this paper is twofold. We first point out that violation of rationality axioms (SARP, GARP, WARP) do not necessarily lead to a nonrational behavior. Second, our tests of axioms SARP, GARP and WARP over a Polish panel data (198790) show that over the 3630 households only 240 violate the three axioms. However these 240 violations are not caused by the nonrespect of demand theory axioms but by the changing of preferences over the period. A logistic regression confirms the robustness of the test since the more the real expenditure increases in absolute value, the more the probability of violating the axioms increases (the respect of the axioms by the 3390 households is not due to an increase of the real expenditure). Moreover, changing in the composition of the family structure increases the probability of being inconsistent. It seems therefore that the 240 apparent violations are due to the appearance of new constraints, which increase the shadow prices of the goods. In order to explain these 240 households’ preference changes, we build an econometric model of prices including an observed monetary component and an unobserved nonmonetary component expressing the constraints faced by the agent. The estimation of this econometric model shows that the agents who apparently violate the axioms have these complete price changes superior to those of the agents who respect the axioms. Thus the agents who apparently violate the axioms faced during the period a change of their nonmonetary resources and the appearance of new constraints. 
Keywords:  Rationality, GARP, Nonparametric tests, Shadow prices. 
Date:  2008–04–01 
URL:  http://d.repec.org/n?u=RePEc:hal:paris1:halshs00268829_v1&r=upt 
By:  Jan Heufer 
Abstract:  This paper explorers rationalizability issues for finite sets of observations of stochastic choice in the framework introduced by Bandyopadhyay et al. (JET, 1999). Is is argued that a useful approach is to consider indirect preferences on budgets instead of direct preferences on commodity bundles. Stochastic choices are rationalizable in terms of stochastic orderings on the normalized price space if and only if there exits a solution to a linear feasibility problem. Together with the weak axiom of stochastic revealed preference the existence of a solution implies rationalizability in terms of stochastic orderings on the commodity space. Furthermore it is shown that the problem of finding sufficiency conditions for binary choice probabilities to be rationalizable bears similarities to the problem considered here. 
Keywords:  Stochastic choice, rationalizability, revealed preference, weak axiom of stochastic revealed preference, revealed favorability 
JEL:  D11 
Date:  2008–09 
URL:  http://d.repec.org/n?u=RePEc:rwi:repape:0070&r=upt 