
on Utility Models and Prospect Theory 
By:  Paolo Ghirardato; Marciano Siniscalchi 
Abstract:  This paper provides a multiplepriors representation of ambiguous beliefs à la Ghirardato, Maccheroni, and Marinacci (2004) and Nehring (2002) for any preference that is (i) monotonic, (ii) Bernoullian, i.e. admits an affine utility representation when restricted to constant acts, and (iii) suitably continuous. Monotonicity is the main substantive assumption: we do not require either Certainty Independence or Uncertainty Aversion. We characterize the set of ambiguous beliefs in terms of ClarkeRockafellar differentials. This allows us to provide an explicit calculation of the set of priors for several recent decision models: multiplier preferences, the smooth ambiguity model, the vector expected utility model, as well as confidence function, variational, general "uncertaintyaverse" preferences, and meandispersion preferences. 
Keywords:  Multiple Priors; Upper and Lower Probabilities; Ambiguity; Monotonic Preferences 
JEL:  D81 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:cca:wpaper:144&r=upt 
By:  Ali alNowaihi; Sanjit Dhami 
Abstract:  We focus on four stylized facts of behavior under risk. Decision makers: (1) Overweight low probabilities and underweight high probabilities. (2) Ignore events of extremely low probability and treat extremely high probability events as certain. (3) Buy inadequate insurance for very low probability events. (4) Keeping the expected loss fixed, there is a probability below which the takeup of insurance drops dramatically. Expected utility (EU) fails on 14. Existing models of rank dependent utility (RDU) and cumulative prospect theory (CP) satisfy 1 but fail on 2, 3, 4. We propose a new class of axiomaticallyfounded probability weighting functions, the composite Prelec weighting functions CPF) that simultaneously account for 1 and 2. When CPF are combined with RDU and CP we get respectively, composite rank dependent utility (CRDU) and composite cumulative prospect theory (CCP). Both CRDU and CCP are able to successfully explain 14. CCP is, however, more satisfactory than CRDU because it incorporates the empirically robust phenomena of reference dependence and loss aversion. 
Keywords:  Decision making under risk; Insurance; Composite Prelec probability weighting functions; Composite rank dependent utility theory; Composite cumulative rospect theory; power invariance; local power invariance 
JEL:  C60 D81 
Date:  2010–04 
URL:  http://d.repec.org/n?u=RePEc:lec:leecon:10/12&r=upt 
By:  Ali alNowaihi; Sanjit Dhami 
Abstract:  Evidence shows that (i) people overweight low probabilities and underweight high probabilities, but (ii) ignore events of extremely low probability and treat extremely high probability events as certain. The main alternative decision theories, rank dependent utility (RDU) and cumulative prospect theory (CP) incorporate (i) but not (ii). By contrast, prospect theory (PT) addresses (i) and (ii) by proposing an editing phase that eliminates extremely low probability events, followed by a decision phase that only makes a choice from among the remaining alternatives. However, PT allows for the choice of stochastically dominated options, even when such dominance is obvious. We propose to combine PT and CP into composite cumulative prospect theory (CCP). CCP combines the editing and decision phases of PT into one phase and does not allow for the choice of stochastically dominated options. This, we believe, provides the best available alternative among decision theories of risk at the moment. As illustrative examples, we also show that CCP allows us to resolve three paradoxes: the insurance paradox, the Becker paradox and the St. Petersburg paradox. 
Keywords:  Decision making under risk; Composite Prelec probability weighting functions; Composite cumulative prospect theory; Composite rank dependent utility theory; Insurance; St. Petersburg paradox; Becker.s paradox 
JEL:  C60 D81 
Date:  2010–04 
URL:  http://d.repec.org/n?u=RePEc:lec:leecon:10/11&r=upt 
By:  Cadogan, Godfrey 
Abstract:  We introduce a monotone class theory of Prospect Theory's value functions, which shows that they can be replaced almost surely by a topological lifting comprised of a class of compact isomorphic maps that embed weakly comonotonic probability measures, attached to state space, in outcome space. Thus, agents solve a signal extraction problem to obtain estimates of empirical probability weights for prospects under risk and uncertainty. By virtue of the topological lifting, we prove an almost sure isomorphism theorem between compact stochastic choice operators, and well defined outcomes which, under BrouwerSchauder theory, guarantees fixed point convergence in convex choice sets. Along the way we introduce a risk operator in the HoffmanJorgensen class of lifting operators, and value function [averaging] operators with respect to Radon measure. In that set up, suitable binary operations on gainloss space show that our risk operator is isometric for gains and skewed for losses. The point spectrum from this operator constitutes the range of admissible observations for loss aversion index in a well designed experiment. 
Keywords:  monotone class theorem; stochastic choice functional; embedded probability; comonotonic probability; isomorphism 
JEL:  D81 C44 C02 
Date:  2010–04–27 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:22380&r=upt 
By:  Flip Klijn (Harvard Business School); Joana Pais (Technical University of Lisbon; UECE–Research Unit on Complexity and Economics); Marc Vorsatz (Fundacion de Estudios de Economia Aplicada (FEDEA)) 
Abstract:  We experimentally investigate in the laboratory two prominent mechanisms that are employed in school choice programs to assign students to public schools. We study how individual behavior is influenced by preference intensities and risk aversion. Our main results show that (a) the GaleShapley mechanism is more robust to changes in cardinal preferences than the Boston mechanism independently of whether individuals can submit a complete or only a restricted ranking of the schools and (b) subjects with a higher degree of risk aversion are more likely to play "safer" strategies under the GaleShapley but not under the Boston mechanism. Both results have important implications for the efficiency and the stability of the mechanisms. 
Keywords:  school choice, risk aversion, preference intensities, laboratory experiment, GaleShapley mechanism, Boston mechanism, efficiency, stability, constrained choice 
JEL:  C78 C91 C92 D78 I20 
Date:  2010–04 
URL:  http://d.repec.org/n?u=RePEc:hbs:wpaper:10093&r=upt 
By:  Sanjit Dhami; Ali alNowaihi 
Abstract:  The Becker proposition (BP) is one of the founding pillars of the modern literature on Law and Economics. It states that it is optimal to impose the severest possible punishment (to maintain effective deterrence) at the lowest possible probability (to economize on enforcement costs). The BP is not consistent with the evidence. This is known as the Becker paradox. Using evidence from a wide range of phenomena we show that none of the proposed explanations for the Becker paradox are satisfactory. The BP has largely been considered within an expected utility framework. We clarify the Becker proposition and its welfare implications under expected utility. We show that BP also holds under rank dependent expected utility and cumulative prospect theory, the two main alternatives to expected utility. alNowaihi and Dhami (2010a) recently propose composite cumulative prospect theory that combines prospect theory with cumulative prospect theory. Under plausible conditions CCP is able to resolve the Becker paradox. Our article opens the way for incorporating nonexpected utility theories into an economic analysis of criminal activity. 
Keywords:  Behavioral economics; Illegal activity; Expected utility theory; Rank dependent expected utility; Prospect theory; Prelec and composite Prelec probability weighting functions; Composite cumulative prospect theory; Punishment functions 
JEL:  D81 K42 
Date:  2010–04 
URL:  http://d.repec.org/n?u=RePEc:lec:leecon:10/14&r=upt 
By:  Franz Dietrich; Christian List 
Date:  2010–04–25 
URL:  http://d.repec.org/n?u=RePEc:cla:levarc:661465000000000046&r=upt 
By:  Cadogan, Godfrey 
Abstract:  We augment Tversky and Khaneman (1992) (“TK92”) Cumulative Prospect Theory (“CPT”) function space with a sample space for “states of nature”, and depict a commutative map of behavior on the augmented space. In particular, we use a homotopy lifting property to mimic behavioral stochastic processes arising from deformation of stochastic choice into outcome. A psychological distance metric (in the class of DudleyTalagrand inequalities) for stochastic learning, was used to characterize stopping times for behavioral processes. In which case, for a class of nonseparable spacetime probability density functions, we find that behavioral processes are uniformly stopped before the goal of fair gamble is attained. Further, we find that when faced with a fair gamble, agents exhibit submartingale [supermartingale] behavior, subjectively, under CPT probability weighting scheme. We show that even when agents’ have classic von NeumanMorgenstern preferences over probability distribution, and know that the gamble is a martingale, they exhibit probability weighting to compensate for probability leakage arising from the their stopped behavioral process. 
Keywords:  commutative prospect theory; homotopy; stopping time; behavioral stochastic process 
JEL:  D81 D70 C0 C02 
Date:  2010–04–26 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:22342&r=upt 
By:  Ali alNowaihi; Sanjit Dhami 
Abstract:  In this paper we begin by stressing the empirical importance of nonlinear weighting of probabilities, which expected utility theory (EU) is unable to accommodate. We then go on to outline three stylized facts on nonlinear weighting that any alternative theory of risk must address. These are that people: overweight small probabilities and underweight large ones (S1); do not choose stochastically dominated options when such dominance is obvious (S2); ignore very small probabilities and code extremely large probabilities as one (S3). We then show that the concept of a probability weighting function (PWF) is crucial in addressing S1S3. A PWF is not, however, a theory of risk. PWF's need to be embedded within some theory of risk in order to have significant predictive content. We ouline the two main alternative theories that are relevant in this regard: rank dependent utility (RDU) and cumulative prospect theory (CP). RDU and CP explain S1,S2 but not S3. We conclude by outlining the recent proposal for composite prospect theory (CPP) that uses the composite Prelec probability weighting function (CPF). CPF is axiomatically founded, and is flexible and parsimonious. CPP can explain all three stylized facts S1,S2,S3. 
Date:  2010–04 
URL:  http://d.repec.org/n?u=RePEc:lec:leecon:10/10&r=upt 
By:  Snowberg, Erik (California Institute of Technology); Wolfers, Justin (Wharton School, University of Pennsylvania) 
Abstract:  The favoritelongshot bias describes the longstanding empirical regularity that betting odds provide biased estimates of the probability of a horse winning – longshots are overbet, while favorites are underbet. Neoclassical explanations of this phenomenon focus on rational gamblers who overbet longshots due to risklove. The competing behavioral explanations emphasize the role of misperceptions of probabilities. We provide novel empirical tests that can discriminate between these competing theories by assessing whether the models that explain gamblers' choices in one part of their choice set (betting to win) can also rationalize decisions over a wider choice set, including compound bets in the exacta, quinella or trifecta pools. Using a new, largescale dataset ideally suited to implement these tests we find evidence in favor of the view that misperceptions of probability drive the favoritelongshot bias, as suggested by Prospect Theory. 
Keywords:  pricing under risk, probability weighting, compound lotteries, favoritelongshot bias 
JEL:  D49 G12 L83 
Date:  2010–04 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp4884&r=upt 
By:  Dalton, P.S.; Ghosal, S. (Tilburg University, Center for Economic Research) 
Abstract:  We relate the normative implications of a model of decisionmaking with endogenous preference parameters to choice theoretic models (Bernheim and Rangel 2007, 2009; Rubinstein and Salant, 2008) in which observed choices are determined by frames or ancillary conditions. 
Keywords:  Decisions;choice;frames;standard;behavioral;welfare. 
JEL:  D01 D62 C61 I30 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:dgr:kubcen:201021&r=upt 
By:  Hao Zhou 
Abstract:  This paper presents predictability evidence from the difference between implied and expected variances or variance risk premium that: (1) the variance difference measure predicts a significant positive risk premium across equity, bond, and credit markets; (2) the predictability is shortrun, in that it peaks around one to four months and dies out as the horizon increases; and (3) such a shortrun predictability is complementary to that of the standard predictor variablesP/E ratio, forward spread, and short rate. These findings are potentially justifiable by a general equilibrium model with recursive preference that incorporates stochastic economic uncertainty. Calibration evidence suggests that such a framework is capable of reproducing the variance premium dynamics, especially its high skewness and kurtosis, without introducing jumps. The calibrated model can also qualitatively explain the equity premium puzzle and the bond risk premia in short horizons. 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:fip:fedgfe:201014&r=upt 
By:  Dalton, P.S.; Ghosal, S. (Tilburg University, Center for Economic Research) 
Abstract:  What are the normative implications of behavioral economics? We study a model where the decisions a person makes, consciously or unconsciously, affect her psycholog ical state (reference point, beliefs, expectations, selfimage) which, in turn, impacts on her ranking over available decisions in the first place. We distinguish between stan dard decisions where the decisionmaker internalizes the feedback from her actions to her psychological state, and behavioral decisions where the psychological state is taken as given (although a decision outcome requires that action and psychological state are mutually consistent). In a behavioral decision, the individual imposes an externality on herself. We provide an axiomatic characterization of behavioral decisions. We show that the testable implications of behavioral and standard decisions are di¤erent and the outcomes of the two decision problems are, typically, distinguishable. We discuss the consequences for public policy of our formal analysis and o¤er normative grounds for subsidized psychological therapies. 
Keywords:  Behavioral Decisions;Welfare;Revealed Preferences;Normative Preferences 
JEL:  D60 I30 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:dgr:kubcen:201022&r=upt 
By:  Karel Báťa (Institute of Economic Studies, Faculty of Social Sciences, Charles University, Prague, Czech Republic) 
Abstract:  Investors reveal a tendency to prefer domestic over foreign equities despite the financial losses. From institutional perspective the factors that cause home biasness are the barriers to entry the foreign markets, transaction costs, illiquidity, asymmetric information and information costs, corporate governance and inflation and exchange rate risks. Behavioral finance argues that irrationality of investors cause the home biasness. Investors tend to be under the influence of psychological biases: optimism, overconfidence, social identity, narrow framing and loss aversion. In this paper we introduce a model of optimal portfolio of Czech investors with three utility functions: Markowitz, exponential and CRRA. The prediction of the model without short selling suggests that Czech investors should have more than 60 % (between 72  83 % for feasible levels of risk aversion) in domestic equities. The OECD data claims that they hold around 87 % in domestic equities. 
Keywords:  Equity home bias, optimal investment portfolio, behavioral finance 
JEL:  G11 
Date:  2010–04 
URL:  http://d.repec.org/n?u=RePEc:fau:wpaper:wp2010_07&r=upt 
By:  Jan Heufer 
Abstract:  Government agencies and other national and international institutions are asked to perform foMit dem nichtparametrischen Ansatz dieser Arbeit lässt sich überprüfen, ob Entscheidungen auf einem Wahrscheinlichkeitssimplex mit quasikonkaven Präferenzen vereinbar sind. Notwendige und hinreichende Bedingungen und Methoden zur Rekonstruierung von Indifferenzkurven werden vorgestellt. Des Weiteren können quasikonkave Nutzenfunktionen in Analogie zur Konstruktion der Nutzenfunktion im Beweis des Theorems von Afriat konstruiert werden. Der Ansatz ist relevant für die Untersuchung von Entscheidungen unter Unsicherheit, stochastischen Entscheidungen und exante Fairness. Die Methode ist besonders für experimentelle Daten geeignet. 
Keywords:  Afriat’s theorem; deterministic preferences; decisions under risk; experimental economcics; nonparametric methods; revealed preference; stochastic choice 
JEL:  C14 C91 D11 D12 
Date:  2010–03 
URL:  http://d.repec.org/n?u=RePEc:rwi:repape:0179&r=upt 
By:  Charles Bellemare (Département d’économique, Université Laval); Alexander Sebald (Department of Economics, University of Copenhagen); Martin Strobel (Department of Economics, Maastricht University) 
Abstract:  We estimate structural models of guilt aversion to measure the population level of willingness to pay (WTP) to avoid feeling guilt by letting down another player. We compare estimates of WTP under the assumption that higherorder beliefs are in equilibrium (i.e. consistent with the choice distribution) with models estimated using stated beliefs which relax the equilibrium requirement. We estimate WTP in the later case by allowing stated beliefs to be correlated with guilt aversion, thus controlling for a possible source of a consensus effect. All models are estimated using data from an experiment of proposal and response conducted with a large and representative sample of the Dutch population. Our range of estimates suggests that responders are willing to pay between 0.40 and 0.80 Euro to avoid letting down proposers by 1 Euro. Furthermore, we find that WTP estimated using stated beliefs is substantially overestimated (by a factor of two) when correlation between preferences and beliefs is not controlled for. Finally, we find no evidence that WTP is significantly related to the observable socioeconomic characteristics of players. 
Keywords:  guilt aversion; willingness to pay; equilibrium and stated beliefs models 
JEL:  C93 D63 D84 
Date:  2010–02 
URL:  http://d.repec.org/n?u=RePEc:kud:kuiedp:1008&r=upt 
By:  Kontek, Krzysztof 
Abstract:  This paper presents a regression procedure for inhomogeneous data characterized by varying variance, skewness and kurtosis or by an unequal amount of data over the estimation domain. The concept is based first on the estimation of the densities of an observed variable for given values of explanatory variable(s). These density functions are then used to estimate the relation between all the variables. The mean, quantile (including median) and mode regression estimators are proposed, with the last one appearing to be the maximum likelihood estimator in the density based approach. The paper demonstrates the advantages of the proposed methodology, which eliminates most of the estimation problems arising from data inhomogeneity. These include the computational inconveniences of the standard quantile and mode regression techniques. The proposed methodology, when applied to lottery experiments, makes it possible to confirm and to extend the previously presented conclusion (Kontek, 2010) that lottery valuations are only nonlinear with respect to probability when medians and means are considered. Such nonlinearity disappears once modes are considered. This means that the most likely behavior of a group is fully rational. The regression procedure presented in this paper is, however, very general and may be applied in many other cases of data inhomogeneity and not just lottery experiments. 
Keywords:  Density Distribution; Least Squares; Quantile; Median; Mode; Maximum Likelihood Estimators; Lottery experiments; Relative Utility Function; Prospect Theory. 
JEL:  C16 C51 D81 C46 C91 C13 C81 C21 C01 D87 
Date:  2010–04–21 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:22268&r=upt 