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on Utility Models and Prospect Theory |
| By: | Moez Abouda (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - 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 bid-selling 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, bid-selling spread, perfect hedging, risk premium. |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:hal:paris1:halshs-00270648_v1&r=upt |
| By: | Thibault Gajdos (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - 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); Jean-Marc Tallon (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Jean-Christophe Vergnaud (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - 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 probability-possibility 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 probability-possibility 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 probability-possibility 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 probability-possibility 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 probability-possibility set, and (ii) shrinking the probability-possibility 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:halshs-00177378_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 Epstein-Zin preferences, there exist plausible parametervalues such that the model generates unconditional mean risk--free 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 price--dividendratio is pro-cyclical 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 risk--free rate with output growth and consumption growth and (ii) the correlation pattern between risk--free 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:2008-14&r=upt |
| By: | Sophie Jallais (PHARE - Pôle d'Histoire de l'Analyse et des Représentations Economiques - CNRS : FRE2541 - Université Panthéon-Sorbonne - Paris I - Université de Paris X - Nanterre); Pierre-Charles Pradier (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, SAMOS - Statistique Appliquée et MOdélisation Stochastique - Université Panthéon-Sorbonne - 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:halshs-00274361_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 self-regulatory resources results in more risk aversion in mixed-gamble (gain/loss) situations. The findings support a dual process view that distinguishes between a rational and an affective information processing system, in which self-regulatory 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: | Rose-Anne 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 Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris) |
| Abstract: | The theory of existence of equilibrium with short-selling 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 short-selling, variational preferences. |
| Date: | 2008–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:paris1:halshs-00281582_v1&r=upt |
| By: | Alain Chateauneuf (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I); Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - 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:halshs-00327700_v1&r=upt |
| By: | Michèle Cohen (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I); Johanna Etner (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, LIRAES - Université Paris Descartes - Paris V); Meglena Jeleva (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - 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:halshs-00211942_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 Panthéon-Sorbonne - Paris I, EEP-PSE - 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 Panthéon-Sorbonne - Paris I, EEP-PSE - 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 : non-dictatorship of the present and non-dictatorship 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 non-dictatorial 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, non-dictatorship of the future, non-dictatorship 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:halshs-00275758_v1&r=upt |
| By: | Julio Davila (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - 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:halshs-00261582_v1&r=upt |
| By: | Thibault Gajdos (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I); Jean-Marc Tallon (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I); Jean-Christophe Vergnaud (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) |
| Abstract: | We axiomatize in the Anscombe–Aumann setting a wide class of preferences called rank-dependent 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 non-neutral 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:halshs-00266049_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); Jean-Marc Tallon (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - 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 re-establish theproposition |
| Keywords: | ambiguity;bid ask spread;Ellsberg paradox |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:hal:paris1:halshs-00175266_v1&r=upt |
| By: | Marc-Arthur 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'Evry-Val d'Essonne); François Gardes (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I); Christophe Starzec (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - 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 non-rational behavior. Second, our tests of axioms SARP, GARP and WARP over a Polish panel data (1987-90) show that over the 3630 households only 240 violate the three axioms. However these 240 violations are not caused by the non-respect 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 non-monetary 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 non-monetary resources and the appearance of new constraints. |
| Keywords: | Rationality, GARP, Non-parametric tests, Shadow prices. |
| Date: | 2008–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:paris1:halshs-00268829_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 |