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on Utility Models and Prospect Theory |
| By: | Monika Bier; Daniel Engelage |
| Abstract: | We consider long-run behavior of agents assessing risk in terms of dynamic convex risk measures or, equivalently, utility in terms of dynamic variational preferences in an uncertain setting. By virtue of a robust representation, we show that all uncertainty is revealed in the limit and agents behave as expected utility maximizer under the true underlying distribution regardless of their initial risk anticipation. In particular, risk assessments of distinct agents converge. This result is a generalization of the fundamental Blackwell-Dubins Theorem, cp. [Blackwell & Dubins, 62], to convex risk. We furthermore show the result to hold in a non -time-consistent environment. |
| Keywords: | Dynamic Convex Risk Measures, Multiple Priors, Uncertainty, Robust Representation, Time-Consistency, Blackwell-Dubins. |
| JEL: | C61 C65 D81 |
| Date: | 2010–05 |
| URL: | http://d.repec.org/n?u=RePEc:bon:bonedp:bgse11_2010&r=upt |
| By: | Frederik Herzberg (Institute of Mathematical Economics, Bielefeld University) |
| Abstract: | It is known that a combination of the Maccheroni-Marinacci-Rustichini (2006) axiomatisation of variational preferences with the Föllmer-Schied (2002,2004) representation theorem for concave monetary utility functionals provides an (individual) decision-theoretic foundation for convex risk measures. The present paper is devoted to collective decision making with regard to convex risk measures and addresses the existence problem for non-dictatorial aggregation functions of convex risk measures - in the guise of variational preferences - satisfying Arrow-type rationality axioms (weak universality, systematicity, Pareto principle). We prove an impossibility result for finite electorates, viz. a variational analogue of Arrow's impossibility theorem. For infinite electorates, the possibility of rational aggregation of variational preferences (i.e. convex risk measures) depends on a uniform continuity condition for the variational preference profiles: We shall prove variational analogues of both Campbell's impossibility theorem and Fishburn's possibility theorem. Methodologically, we adopt the model-theoretic approach to aggregation theory inspired by Lauwers-Van Liedekerke (1995). In an appendix, we apply the Dietrich-List (2010) analysis of logical aggregation based on majority voting to the problem of variational preference aggregation. The fruit is a possibility theorem, but at the cost of considerable and - at least at first sight - rather unnatural restrictions on the domain of the variational preference aggregator. |
| Keywords: | variational preference representation, convex risk measure, multiple priors preferences, Arrow-type preference aggregation, judgment aggregation, abstract aggregation theory, model theory, first-order predicate logic, ultrafilter, ultraproduct |
| JEL: | D71 G11 |
| Date: | 2010–05 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:432&r=upt |
| By: | Schipper, Burkhard (University of California, Davis) |
| Abstract: | I develop awareness-dependent subjective expected utility by taking unawareness structures introduced in Heifetz, Meier, and Schipper (2006, 2008, 2009) as primitives in the Anscombe-Aumann approach to subjective expected utility. I observe that a decision maker is unaware of an event if and only if her choices reveal that the event is "null" and the negation of the event is "null". Moreover, I characterize "impersonal" expected utility that is behaviorally indistinguishable from awareness-dependent subject expected utility and assigns probability zero to some subsets of states that are not necessarily events. I discuss in what sense impersonal expected utility can not represent unawareness. |
| JEL: | C70 C72 D80 D82 |
| Date: | 2010–03 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:ucdeco:10-5&r=upt |
| By: | Sharma, Tridib; Vadovic, Radovan |
| Abstract: | The Axiom of Monotonicity (AM) is a necessary condition for a number of expected utility representations, including those obtained by de Finetti (1930), von Neumann and Morgenstern (1944) and Savage (1954). The paper reports on experiments that directly test AM by eliminating strategic uncertainty, context, and peer effects. In this sterile and simple environment we do not observe AM violations under uncertainty but we do observe violations under ambiguity. |
| Keywords: | monotonicity; dominance; disjunction effect; sure thing principle |
| JEL: | D81 C91 C72 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:22863&r=upt |
| By: | Kontek, Krzysztof |
| Abstract: | This paper discusses two approaches for the analysis of multi-outcome lotteries. The first uses Cumulative Prospect Theory. The second is the Relative Utility Function, which strongly resembles the utility function hypothesized by Markowitz (1952). It is shown that the relative utility model follows Expected Utility Theory with a transformed outcome domain. An illustrative example demonstrates that not only it is a simpler model, but it also provides more sound predictions regarding certainty equivalents of multi-outcome lotteries. The paper discusses estimation procedures for both models. It is noted that Cumulative Prospect Theory has been derived using two-outcome lotteries only, and it is hard to find any evidence in the literature of its parameters ever having been estimated by using lotteries with more than two outcomes. Least squares (mean) and quantile (including median) regression estimations are presented for the relative utility model. It turns out that the estimations for two- and three-outcome lotteries are essentially the same. This confirms the correctness of the model and vindicates the homogeneity of responses given by subjects. An additional advantage of the relative utility model is that it allows multi-outcome lotteries, together with the estimation results, to be presented on a single graph. This is not possible using Cumulative Prospect Theory. |
| Keywords: | Multi-Prize Lotteries; Lottery / Prospect Valuation; Markowitz Hypothesis; Prospect / Cumulative Prospect Theory; Aspiration / Relative Utility Function. |
| JEL: | C13 C51 D81 C21 C91 D87 |
| Date: | 2010–05–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:22947&r=upt |
| By: | Simonson, Itamar (Stanford University); Sela, Aner (Stanford University) |
| Abstract: | Despite the very long history of research on heritable traits, we still know very little about genetic effects on judgment and choice, including consumer decision making. Building on recent advances in epigenetics, we hypothesize that people inherit a general prudence tendency, which affects their predisposition to choose options that vary on the prudence dimension. We use a classic twins study design whereby greater similarity between monozygotic twins than between dizygotic twins indicates a heritable trait. Unlike most prior studies that have focused on one or few characteristics, our study examines a broad range of judgment and choice phenomena simultaneously in order to gain insights into heritable tendencies (representing individual differences) and nonheritable tendencies. Consistent with our "prudence hypothesis," we find a significant heritable effect on (a) preferences for compromise (but not perceptually dominating) options, (b) choosing a sure gain over a gamble, (c) preferences for a feasible though dull assignment (in the near distance), (d) maximizing (versus satisficing), and (e) preferences for utilitarian (versus hedonic) options. Conversely, non-prudence problems (e.g., relating to discounting, highlighting, variety) as well as judgment heuristics (availability, representativeness, anchoring) do not appear to reflect heritable individual differences. We discuss the implications of our research with respect to the determinants of preferences, the interpretation of rationality and of BDT effects, the notion of constructive predispositions, and directions for future research regarding the role of genetics in decision making. |
| Date: | 2009–07 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:2029&r=upt |
| By: | Giuseppe Migali |
| Abstract: | Individual risk aversion and riskiness of investment in higher education are combined with two alternative loan-based financing systems, income contingent loans (ICL) and mortgage loans (ML), to investigate the effects on graduate lifetime expected utilities. We deal explicitly with the presence of hidden subsidies due to discounting, which is one of the main drawbacks of an ICL. The theoretical model has been calibrated using real data on graduate earnings and their volatility, together with the features of the English HE financing system, which has recently switched from a ML to an ICL system. Higher uncertainty in earnings in general makes an ICL the preferred system for risk averse individuals, while risk neutral individuals prefer mortgage loans. |
| Keywords: | Education Choice; Risk Aversion; Uncertainty |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:lan:wpaper:006705&r=upt |
| By: | Menkhoff, Lukas |
| Abstract: | This paper examines the puzzlingly high unexploited momentum returns from a new perspective. We analyze characteristics of momentum traders in a sample of 692 fund managers. We find that momentum traders are "defined" by their short-term horizon, by a behavioural view on the market and by a somewhat lower degree of risk aversion, whereas they are like other fund managers with respect to sophistication. This is consistent with the interpretation that momentum returns may compensate for the risk of momentum trading on short-term horizons and that the short-term oriented momentum traders are not in a position to perform long-term arbitrage. |
| Keywords: | momentum trading, market efficiency, behavioural finance, risk |
| JEL: | G14 G23 D85 |
| Date: | 2010–05 |
| URL: | http://d.repec.org/n?u=RePEc:han:dpaper:dp-448&r=upt |
| By: | Salvador Barberà; Dolors Berga; Bernardo Moreno |
| Abstract: | We characterize the set of all individual and group strategy-proof rules on the domain of all single-dipped preferences on a line. For rules defined on this domain, and on several of its subdomains, we explore the implications of these strategy-proofness requirements on the maximum size of the rules' range. We show that when all single-dipped preferences are admissible, the range must contain two alternatives at most. But this bound changes as we consider different subclasses of single-dipped preferences: we provide examples of subdomains admitting strategy-proof rules with larger ranges. We establish exact bounds on the maximal size of strategy-proof functions on each of these domains, and prove that the relationship between the sizes of the subdomains and those of the ranges of strategy-proof functions on them need not be monotonic. Our results exhibit a sharp contrast between the structure of strategy-proof rules defined on subdomains of single-dipped preferences and those defined on subsets of single-peaked ones. |
| Keywords: | strategy-proof, group strategy-proof, binary range rules, single-dipped |
| JEL: | D71 |
| Date: | 2009–12–31 |
| URL: | http://d.repec.org/n?u=RePEc:aub:autbar:801.09&r=upt |
| By: | Dreber, Anna (Harvard U); Rand, David G. (Harvard U); Garcia, Justin R. (Binghamton U, SUNY); Wernerfelt, Nils (Harvard U); Lum, J. Koji (Binghamton U, SUNY); Zeckhauser, Richard (Harvard U) |
| Abstract: | Individuals differ significantly in their willingness to take risks. Such differences may stem, at least in part, from individual biological (genetic) differences. We explore how risk-taking behavior varies with different versions of the dopamine receptor D4 gene (DRD4), which has been implicated in previous studies of risk taking. We investigate risk taking in three contexts: economic risk taking as proxied by a financial gamble, self-reported general risk taking, and self-reported behavior in risk-related activities. Our participants are serious tournament bridge players with substantial experience in risk taking. Presumably, this sample is much less varied in its environment than a random sample of the population, making genetic-related differences easier to detect. A prior study (Dreber et al. 2010) looked at risk taking by these individuals in their bridge decisions. We examine their risk decisions in other contexts. We find evidence that individuals with a 7-repeat allele (7R+) of the DRD4 genetic polymorphism take significantly more economic risk in an investment game than individuals without this allele (7R-). Interestingly, this positive relationship is driven by the men in our study, while the women show a negative but non-significant result. Even though the number of 7R+ women in our sample is low, our results may indicate a gender difference in how the 7R+ genotype affects behavior, a possibility that merits further study. Considering other risk measures, we find no difference between 7R+ and 7R- individuals in general risk taking or any of the risk-related activities. Overall, our results indicate that the dopamine system plays an important role in explaining individual differences in economic risk taking in men, but not necessarily in other activities involving risk. |
| JEL: | C91 C93 D81 D87 G00 |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:harjfk:rwp10-012&r=upt |
| By: | Jose Apesteguia; Miguel Angel Ballester |
| Abstract: | There is ample evidence to show that choice behavior often deviates from the classical principle of maximization. This evidence raises at least two important questions: (i) how severe the deviation is and (ii) which method is the best for extracting relevant information from the choices of the individual for the purposes of welfare analysis. In this paper we address these two questions by proposing a set of foundational conditions on which to build a proper measure of the rationality of individuals, and enable individual welfare analysis of potentially inconsistent subjects, all based on standard revealed preference data. In our first result, we show that there is a unique measure of rationality that satisfies all of the proposed axioms: the weighted-loss indices. In the second part of the paper, we study some relevant properties of weighted-loss indices. |
| Keywords: | Rationality; Individual Welfare; Revealed Preference. |
| JEL: | D01 D60 |
| Date: | 2010–05 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1220&r=upt |
| By: | Carl Chiarella (School of Finance and Economics, University of Technology, Sydney); Roberto Dieci (Department of Mathematics for Economics and Social Sciences, University of Bologna); Xue-Zhong He (School of Finance and Economics, University of Technology, Sydney) |
| Abstract: | By taking into account conditional expectations and the dependence of the systematic risk of asset returns on micro- and macro-economic factors, the conditional CAPM with time-varying betas displays superiority in explaining the cross-section of returns and anomalies in a number of empirical studies. Most of the literature on time-varying beta is motivated by econometric estimation rather than explicit modelling of the stochastic behaviour of betas through agents’ behaviour. Within the mean-variance framework of repeated one-period optimisation, we set up a boundedly rational dynamic equilibrium model of a ï¬nancial market with heterogeneous agents and obtain an explicit dynamic CAPM relation between the expectede quilibrium returns and time-varying betas. By incorporating the three most popular types of investors, fundamentalists, chartists and noise traders, into the model, we show that, independent of the fundamentals, there is a systematic change in the market portfolio, risk-return relationships, and time varying betas when investors change their behaviour, such as the chartists acting as momentum traders. In particular, we demonstrate the stochastic nature of time-varying betas and show that the commonly used rolling window estimates of time-varying betas may not be consistent with the ex-ante betas implied by the equilibrium model. The results provide a number of insights into an understanding o ftime-varying beta. |
| Keywords: | equilibrium asset prices; CAPM; time-varying betas, heterogeneous expectations |
| JEL: | G12 D84 |
| Date: | 2010–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:uts:rpaper:275&r=upt |