
on Utility Models and Prospect Theory 
By:  Simone CerreiaVioglio (Department of Decision Sciences, Universit_a Bocconi); David Dillenberger (Department of Economics, University of Pennsylvania); Pietro Ortoleva (Department of Economics, Columbia University) 
Abstract:  Many violations of the Independence axiom of Expected Utility can be traced to subjects' attraction to riskfree prospects. Negative Certainty Independence, the key axiom in this paper, formalizes this tendency. Our main result is a utility representation of all preferences over monetary lotteries that satisfy Negative Certainty Independence together with basic rationality postulates. Such preferences can be represented as if the agent were unsure of how risk averse to be when evaluating a lottery p; instead, she has in mind a set of possible utility functions over outcomes and displays a cautious behavior: she computes the certainty equivalent of p with respect to each possible function in the set and picks the smallest one. The set of utilities is unique in a welldefined sense. We show that our representation can also be derived from a `cautious' completion of an incomplete preference relation. 
Keywords:  Preferences under risk, Allais paradox, Negative Certainty Independence, Incomplete preferences, Cautious Completion, MultiUtility representation. 
JEL:  D80 D81 
Date:  2013–07–09 
URL:  http://d.repec.org/n?u=RePEc:pen:papers:13037&r=upt 
By:  David Crainich (CNRSLEM and IESEG School of Management); Louis Eeckhoudt (IESEG School of Management (LEMCNRS) and and CORE (Université Catholique de Louvain)); James K. Hammitt (Harvard University (Center for Risk Analysis), Cambridge  Toulouse School of Economics (LERNAINRA)) 
Abstract:  The relationship between willingness to pay (WTP) to reduce the probability of an adverse event and the degree of risk aversion is ambiguous. The ambiguity arises because paying for protection worsens the outcome in the event the adverse event occurs, which influences the expected marginal utility of wealth. Using concepts of prudence (equivalently, downside risk aversion), we characterize the marginal WTP to reduce the probability of the adverse event as the product of WTP in the case of risk neutrality and an adjustment factor. For the univariate case (e.g., risk of financial loss), the adjustment factor depends on risk aversion and prudence with respect to wealth. For the bivariate case (e.g., risk of death or illness), the adjustment factor depends on risk aversion and crossprudence in wealth. 
Keywords:  value per statistical life, mortality risk, risk aversion, prudence 
JEL:  D8 I1 
Date:  2013–06 
URL:  http://d.repec.org/n?u=RePEc:ies:wpaper:e201313&r=upt 
By:  David Crainich (CNRSLEM and IESEG School of Management); Louis Eeckhoudt (IESEG School of Management (LEMCNRS) and and CORE (Université Catholique de Louvain)); Olivier Le Courtois (EM Lyon Business School) 
Abstract:  The concept of absolute risk aversion proposed by K. Arrow (1965) and J. Pratt (1964) and the assumption that it is decreasing in wealth has played a central role in the analysis of risky choices. Ten years later S. Richard (1975) defined correlation aversion in the framework of bivariate utility functions. Surprisingly however the measure of the intensity of correlation aversion has received so far almost no attention. In this paper we define an index of (absolute) correlation aversion and stress some of its properties. Besides we show how the assumption that it is decreasing in wealth generates new results for the analysis of risky choices under bivariate utility. Finally we indicate how these notions can be extended to higher orders of risk attitudes. 
Keywords:  Correlation aversion 
JEL:  D81 
Date:  2013–06 
URL:  http://d.repec.org/n?u=RePEc:ies:wpaper:e201312&r=upt 
By:  Marcel Nutz 
Abstract:  We give a general formulation of the utility maximization problem under nondominated model uncertainty in discrete time and show that an optimal portfolio exists for any utility function that is bounded from above. In the unbounded case, integrability conditions are needed as nonexistence may arise even if the value function is finite. 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1307.3597&r=upt 
By:  CamposVazquez, Raymundo M.; Cuilty, Emilio 
Abstract:  This study measures risk and loss aversion using Prospect Theory and the impact of emotions on those parameters. Our controlled experiment at two universities in Mexico City, using uncompensated students as research subjects, found results similar to those obtained by Tanaka et al. (2010). In order to study the role of emotions, we provided subjects with randomly varied information on rising deaths due to drug violence in Mexico and also on youth unemployment. In agreement with previous studies, we find that risk aversion on the gains domain decreases with age and income. We also find that loss aversion decreases with income and is less for students in public universities. With regard to emotions, risk aversion increases with sadness and loss aversion is negatively influenced by anger. On the loss domain, anger dominates sadness. On average, anger reduces loss aversion by half. 
Keywords:  Risk Aversion; Emotions; Prospect Theory; Experiment; Mexico 
JEL:  C93 D03 D12 O12 O54 
Date:  2013–03 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:48280&r=upt 
By:  Erhan Bayraktar; Zhou Zhou 
Abstract:  We consider the robust utility maximization using a static holding in derivatives and a dynamic holding in the stock. There is no fixed model for the price of the stock but we consider a set of probability measures (models) which are not necessarily dominated by a fixed probability measure. By assuming that the set of physical probability measures is convex and weakly compact, we obtain the duality result and the existence of an optimizer. 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1307.4813&r=upt 
By:  Iñigo IturbeOrmaetxe Kortajarene (Universidad de Alicante); Giovanni Ponti (Universidad de Alicante); Josefa Tomás (Universidad de Alicante) 
Abstract:  Experimental evidence suggests that the frequency with which individuals get feedback information on their investments has an effect on risktaking behavior. In particular, when they are given information sufficiently often, they take fewer risks compared with a situation in which they are informed less frequently. In this paper we find that this result still holds when subjects do not know the probabilities of the lotteries they are betting upon. We also detect significant gender effects, in that the frequency with which information is disclosed mostly affects men’s betting behavior, rather than women’s, and that men are much more riskseeking after experiencing a loss. 
Keywords:  Myopic loss aversion, evaluation periods, ambiguity, gender effects 
JEL:  C91 D81 D14 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:ivi:wpasad:201305&r=upt 
By:  Kohei Daido (School of Economics, Kwansei Gakuin University); Takeshi Murooka (Department of Economics, University of California, Berkeley) 
Abstract:  We investigate moralhazard problems with limited liability where agents have expectationbased referencedependent preferences. We show that stochastic compensation for low performance can be optimal. Because of loss aversion, the agents have firstorder risk aversion to wage uncertainty. This causes the agents to work harder when their low performance is stochastically compensated. We also examine team incentives for credibly employing such stochastic compensation. In an optimal contract, low and highperformance agents are equally rewarded if most agents achieve high performance. Team incentives can be optimal even when there are only two agents and the degree of loss aversion is not large. 
Keywords:  Moral Hazard, Loss Aversion, Stochastic Compensation, Team Incentives,ReferenceDependent Preferences 
JEL:  D03 D86 M12 M52 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:kgu:wpaper:107&r=upt 
By:  Groneck, Max; Ludwig, Alexander; Zimper, Alexander (Munich Center for the Economics of Aging (MEA)) 
Abstract:  On average, "young" people underestimate whereas "old" people overestimate their chances to survive into the future. We adopt a Bayesian learning model of ambiguous survival beliefs which replicates these patterns. The model is embedded within a nonexpected utility model of lifecycle consumption and saving. Our analysis shows that agents with ambiguous survival beliefs (i) save less than originally planned, (ii) exhibit undersaving at younger ages, and (iii) hold longer on to their assets than their rational expectations counterparts who correctly assess survival probabilities. Our ambiguitydriven model therefore simultaneously accounts for three important empirical fi…ndings on household saving behavior. 
JEL:  D91 D83 E21 
Date:  2013–07–02 
URL:  http://d.repec.org/n?u=RePEc:mea:meawpa:13270&r=upt 
By:  Jeff Birchby (Rutgers University); Gary Gigliotti (Rutgers University); Barry Sopher (Rutgers University) 
Abstract:  It is common in studies of individual choice behavior to report averages of the behavior under consideration. In the social sciences the mean is, indeed, often the quantity of interest, but at times focusing on the mean can be misleading. For example, it is well known in labor economics that failure to account for individual differences may lead to incorrect inference about the nature of hazard functions for unemployment duration. If all workers have constant hazard functions independent of duration, simple aggregation will nonetheless lead to the inference that the hazard function is statedependent, with the hazard of leaving unemployment declining with duration of unemployment. Similarly, a recent study in psychology has shown that the “learning curve,” a monotonically increasing function of response to a stimuli, is better understood as an average representation of individual response functions that are, in fact, more stepfunctionlike. As such, the learning curve as commonly understood is a misleading representation of the behavior of any one individual. These observations motivate us to consider the question of possible aggregation bias in the realm of choice under uncertainty. In particular, Cumulative Prospect Theory posits a weighting function through which probabilities are transformed into decision weights. An inverted Sshaped weighting function is commonly taken to be “the” appropriate weighting function, based on quite a number of experimental studies. This particular version of the weighting function implies, in simple two outcome lotteries, that an individual will tend to overweight small (near 0) probabilities and to underweight large (near 1) probabilities. A natural question to ask, suggested by both the hazard function and the learning curve examples, is whether this weighting function is not, similarly, an artifact of aggregation. Of course, no one believes that every individual’s behavior can be accounted for by a single weighting function. Studies have shown that there can be considerable variation in estimated weighting functions across individuals. But no one, to our knowledge, has systematically addresses the question of whether, in fact, one can meaningfully use a single weighting function, even as a rhetorical device, to accurately discuss individual choice behavior. If most individuals indeed do have an inverted Sshaped weighting function, then this representation of choice behavior is not misleading, provided it is clear that one is discussing the behavior of “most,” not all, individuals. We focus on the reliability of estimated weighting functions. We study the problem of determining the parameters of the cumulative prospect theory function. Using responses to paired sets of choice questions, it is possible to derive estimates for a twoparameter version of the Cumulative Prospect Theory choice function (using a power function for the value function and Prelec’s one parameter version of the weighting function). By analyzing multiple such pairs of choice questions, we are able to also investigate the consistency of these estimates. Our main finding is that there is, in general, considerable variation at the individual level in the choice parameters implied by the responses to the different pairs of choice questions. The modal choice pattern observed is one consistent with expected value maximization, and there is considerably less variation (again, at the individual level) in the parameters implied by those who appear to be maximizing expected value on one pair of choice questions than for those who never choose in this way. But these individuals account for only about onefifth to onesixth of subjects. For the rest of the subjects, it is rare that any two pairs of estimates are the same, and often the implied parameters 
Keywords:  uncertainty, prospect theory, aggregation, consistency 
JEL:  C9 D8 
Date:  2013–01–18 
URL:  http://d.repec.org/n?u=RePEc:rut:rutres:201301&r=upt 
By:  Gul, Ejaz 
Abstract:  Investment in long lived projects such as buildings are characterized by uncertainties regarding project life, operation and maintenance costs, revenues and other factors that affect project economics. Since the exact values of these variable factors are usually unknown, it is difficult to make economic evaluations with a high degree of reliability. A common approach to project investment analysis is to apply the economic methods for estimates of project input variables and to present results in single value, deterministic terms. Yet failures to account for uncertain input variables expose the decision makers to risk. Current research is about quantifying the economic risk exposure of the projects and willingness of investors to take a chance on an investment of uncertain outcome based on risk attitude. Paper explains typical investment situations of decision makers who do not know with certainty the outcome of their investment and illustrates with probability distribution a way of measuring risk exposure and introduces the use of utility functions to determine a decision maker’s risk attitude. It is concluded from the study that to determine the true value of investments for risk takers, economic analysis must account for increasing marginal satisfaction of higher payoffs with corresponding increases in marginal utility. A firm or institution can use utility theory in a normative or prescriptive role to establish risk policy for investments that support the firm’s or institution’s risk attitude. Overall the paper provides a useful study on economic risk exposure of projects and risk attitudes of investors in Monrovia, the capital of Liberia. 
Keywords:  Investment, economic, risk exposure, probability function, risk attitude, utility function. 
JEL:  G30 G32 
Date:  2013–07–09 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:48221&r=upt 
By:  Giuseppe Benedetti; Luciano Campi 
Abstract:  We consider the problem of exponential utility indifference valuation under the simplified framework where traded and nontraded assets are uncorrelated but where the claim to be priced possibly depends on both. Traded asset prices follow a multivariate Black and Scholes model, while nontraded asset prices evolve as generalized OrnsteinUhlenbeck processes. We provide a BSDE characterization of the utility indifference price (UIP) for a large class of nonsmooth, possibly unbounded, payoffs depending simultaneously on both classes of assets. Focusing then on European claims and using the Gaussian structure of the model allows us to employ some BSDE techniques (in particular, a Malliavintype representation theorem due to Ma (2002)) to prove the regularity of Z and to characterize the UIP for possibly discontinuous European payoffs as a viscosity solution of a suitable PDE with continuous space derivatives. The optimal hedging strategy is also identified essentially as the delta hedging strategy corresponding to the UIP. Since there are no closedform formulas in general, we also obtain asymptotic expansions for prices and hedging strategies when the risk aversion parameter is small. Finally, our results are applied to pricing and hedging power derivatives in various structural models for energy markets. 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1307.4591&r=upt 
By:  Ronald J. Degen (International School of Management Paris) 
Abstract:  Wisdom, uncertainty, and ambiguity will always exist in management decisions. One danger for firms lies in managers making decisions that are based on faulty theories acquired through personal experience or learned from experience of others. Often, these decisions don’t generate the expected outcome and may even put the future of the firm at risk. To avoid this risk, managers are required to become wiser, more discerning, and more appropriately skeptical toward simplistic formulas and quickfix remedies (as explained by Rosenzweig, 2007). In this paper, the author discusses types of business research and their philosophical assumptions, the strength and weaknesses of qualitative and quantitative research methods, the benefits of combining both methods, and the trustworthiness of research methods in general for validating the management theories used by managers in their decisionmaking. 
Keywords:  management decisions, business research methods, risk of faulty theories, wisdom in management decisions 
JEL:  M0 M1 
Date:  2013–07–17 
URL:  http://d.repec.org/n?u=RePEc:pil:wpaper:94&r=upt 
By:  Gul, Ejaz 
Abstract:  Utility, Rationality and Methodological Individualism (URMI) are the dominant aspects which determine the paradigm of ethics applicable in economic decision making process. Generally, in traditional economics the decisionmaking process for individuals has no significant space for ethics as individuals are only interested in maximizing their profits. URMI is a very important concept the formulation of which into various combinations determines different functions for ethics in economics. Economists have used different definitions for the constituents of this concept but there can not be sighted noteworthy effort to integrate these multi dimensional phenomena into a framework for ethics in economics. This paper integrates different approaches about URMI and chalk out a framework for incorporating ethics into economics. 
Keywords:  Ethics, utility, methodological individualism, framework, economics 
JEL:  D6 D71 Z13 
Date:  2013–07–15 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:48344&r=upt 
By:  Zumbühl, Maria (ROA, Maastricht University); Dohmen, Thomas (University of Bonn); Pfann, Gerard A. (Maastricht University) 
Abstract:  We study empirically whether there is scope for parents to shape the economic preferences and attitudes of their children through purposeful investments. We exploit information on the risk and trust attitudes of parents and their children, as well as rich information about parental efforts in the upbringing of their children from the German SocioEconomic Panel Study. Our results show that parents who invest more in the upbringing of their children are more similar to them with respect to risk and trust attitudes and thus transmit their own attitudes more strongly. The results are robust to including variables on the relationship between children and parents, family size, and the parents' socioeconomic background. 
Keywords:  risk preferences, trust, intergenerational transmission, cultural transmission, social mobility, GSOEP 
JEL:  D1 D8 J13 J62 Z13 
Date:  2013–06 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp7476&r=upt 
By:  Avdic, Daniel (Uppsala University); Johansson, Per (IFAU) 
Abstract:  Women are on average more absent from work for health reasons than men. At the same time, they live longer. This conflicting pattern suggests that part of the gender difference in healthrelated absenteeism arises from differences between the genders unrelated to actual health. An overlooked explanation could be that men and women's preferences for absenteeism differ, for example because of gender differences in risk preferences. These differences may originate from the utilitymaximizing of households in which women's traditional dual roles influence household decisions to invest primarily in women's health. Using detailed administrative data on sick leave, hospital visits and objective health measures we first investigate the existence of genderspecific preferences for absenteeism and subsequently test for the household investment hypothesis. We find evidence for the existence of gender differences in preferences for absence from work, and that a nontrivial part of these preference differences can be attributed to household investments in women's health. 
Keywords:  sickness absence, gender norms, health investments 
JEL:  J22 D13 
Date:  2013–06 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp7480&r=upt 
By:  Roemer, John E. 
Abstract:  Economic development should be conceived of as the degree to which an economy has implemented an efficient and just distribution of economic resources. The ubiquitous measure of GDP per capita reflects a utilitarian conception of justice, where individual utility is defined as personal income, and social welfare is the average of utilities in a population. A more attractive conception of justice is opportunityequalization. Here, a twodimensional measure of economic development is proposed, based upon viewing individuals’ incomes as a consequence of circumstances, effort, and policy. The first dimension is the average income level of those in the society with the most disadvantaged circumstances, and the second dimension is the degree to which total income inequality is due to differential effort, as opposed to differential circumstances. This pair of numbers is computed for a set of 22 European countries. No country dominates all others on both dimensions. The twodimensional measure induces a partial ordering of countries with respect to development. 
Keywords:  Economic Theory&Research,Inequality,Population Policies,Rural Poverty Reduction,Poverty Impact Evaluation 
Date:  2013–07–01 
URL:  http://d.repec.org/n?u=RePEc:wbk:wbrwps:6530&r=upt 