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on Utility Models and Prospect Theories |
| By: | Robert J. Aumann (Hebrew University of Jerusalem); Roberto Serrano (Brown University) |
| Abstract: | Define the riskiness of a gamble as the reciprocal of the absolute risk aversion (ARA) of an individual with constant ARA who is indifferent between taking and not taking that gamble. We characterize this index by axioms, chief among them a \"duality\" axiom which, roughly speaking, asserts that less risk-averse individuals accept riskier gambles. The index is homogeneous of degree 1, monotonic with respect to first and second order stochastic dominance, and for gambles with normal distributions, is half of variance/mean. Examples are calculated, additional properties derived, and the index is compared with others in the literature. |
| Keywords: | riskiness; risk aversion; expected utility; decision making |
| JEL: | C00 C43 D00 D80 D81 E44 G00 |
| Date: | 2007–02–28 |
| URL: | http://d.repec.org/n?u=RePEc:imd:wpaper:wp2007-08&r=upt |
| By: | John D Hey; Andrea Morone; Ulrich Schmidt |
| Abstract: | In the context of eliciting preferences for decision making under risk, we ask the question: "which might be the 'best' method for eliciting such preferences?". It is well known that different methods differ in terms of the bias in the elicitation; it is rather less well-known that different methods differ in terms of their noisiness. The optimal trade-off depends upon the relative magnitutdes of these two effects. We examine four different elicitation mechanisms (pairwise choice, willingness-to-pay, willingness-to-accept, and certainty equivalents) and estimate both effect. Our results suggest that economists might be better advised to use what appears to be a relatively inefficient elicitation technique (i.e. pairwise choice) in order to avoid trhe bias in better-known and more widely-used techniques. |
| Keywords: | Pairwise choice, willingness-to-pay, willingness-to-accept, errors, noise, biases |
| JEL: | C91 C81 |
| Date: | 2007–02 |
| URL: | http://d.repec.org/n?u=RePEc:yor:yorken:07/04&r=upt |
| By: | Harin, Alexander |
| Abstract: | The principle of uncertain future: the probability of a future event contains a degree of (hidden) uncertainty. As a result, this uncertainty (in a sense, similar to vibrations, fluctuations) pushes the probability value back from the bounds to the middle of its range (from ~100% and ~0% to the middle probability values). In other words, the real values of high probabilities are lower than the preliminarily determined ones. Conversely, the real values of low probabilities are higher than the preliminarily determined ones. This result provides the uniform solution of a number of fundamental problems: the underweighting of high and the overweighting of low probabilities, the Allais paradox, risk aversion, loss aversion, the Ellsberg paradox, the equity premium puzzle, etc. The principle and its consequences can be applied in the fields of banking, investment, insurance, trade, industry, planning and forecasting. Explanations of the principle and examples of solution of three types of basic utility problems are provided. |
| Keywords: | risk; market; banking; industry; development; investments; insurance; hidden causes |
| JEL: | D8 A1 E22 G22 C7 |
| Date: | 2007–02–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:1959&r=upt |
| By: | Thibault Gajdos (CES - Centre d'économie de la Sorbonne - [CNRS : UMR8174] - [Université Panthéon-Sorbonne - Paris I]); Takashi Hayashi (Department of Economics, University of Texas - [University of Texas at Austin]); 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: | This paper presents an axiomatic model of decision making which incorporates objective but imprecise information. We axiomatize a decision criterion of the multiple priors (or maxmin expected utility) type. The model achieves two primary objectives. First, it explains how subjective belief varies with information. Second, it identifies an explicit attitude toward imprecision that underlies usual hedging axioms. 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. She is assumed to rank pairs of the form (P,f) where P is a probability-possibility set and f is an act mapping states into outcomes. The representation result delivers multiple-priors utility at each probability-possibility set. There is a mapping that gives for each probability-possibility set the subjective set of priors. This allows both subjective expected utility when the subjective set of priors is reduced to a singleton and the other extreme where the decision maker takes the worst case scenario in the entire probability-possibility set. We show that the relation «more averse to imprecision» is characterized by inclusion of the sets of priors, irrespective of the utility functions that capture risk attitude. We characterize, under extra axioms, a more precise functional form, in which the subjective set of priors 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 preference. |
| Keywords: | Imprecise information, imprecision aversion, multiple priors, Steiner point. |
| Date: | 2007–02–09 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00130179_v1&r=upt |
| By: | Philipp C. Wichardt (Economic Theory 3, University of Bonn, Adenauerallee 24-26, D-53113 Bonn, Germany. philipp.wichardt@uni-bonn.de.) |
| Abstract: | This paper provides an argument for the advantage of a preference for identity-consistent behaviour from an evolutionary point of view. Within a stylised model of social interaction, we show that the development of cooperative social norms is greatly facilitated if the agents of the society possess a preference for identity consistent behaviour. As cooperative norms have a positive impact on aggregate outcomes, we conclude that such preferences are evolutionarily advantageous. Furthermore, we discuss how such a preference can be integrated in the modelling of utility in order to account for the distinctive cooperative trait in human behaviour and show how this squares with the evidence. |
| Keywords: | cognitive dissonance, fairness, identity, reciprocity, social Norms, social preferences, utility |
| JEL: | A13 C70 C90 D01 Z13 |
| Date: | 2007–01 |
| URL: | http://d.repec.org/n?u=RePEc:trf:wpaper:193&r=upt |
| By: | Wolfram J. Horneff (Johann Wolfgang Goethe-University of Frankfort); Raimond Maurer (Johann Wolfgang Goethe-University of Frankfort); Olivia S. Mitchell (Wharton School, University of Pennsylvania); Ivica Dus (Johann Wolfgang Goethe-University of Frankfort) |
| Abstract: | Retirees must draw down their accumulated assets in an orderly fashion so as not to exhaust their funds too soon. We derive the optimal retirement portfolio from a menu that includes payout annuities as well as an investment allocation and a withdrawal strategy, assuming risk aversion, stochastic capital markets, and uncertain lifetimes. The resulting portfolio allocation, when fixed as of retirement, is then compared to phased withdrawal strategies such a "self-annuitization" plan or the 401(k) "default" pattern encouraged under US tax law. Surprisingly, the fixed percentage approach proves appealing for retirees across a wide range of risk preferences, supporting financial planning advisors who often recommend this rule. We then permit the retiree to switch to an annuity later, which gives her the chance to invest in the capital market and "bet on death." As risk aversion rises, annuities first crowd out bonds in retiree portfolios; at higher risk aversion still, annuities replace equities in the portfolio. Making annuitization compulsory can also lead to substantial utility losses for less risk-averse investors. |
| Date: | 2006–07 |
| URL: | http://d.repec.org/n?u=RePEc:mrr:papers:wp124&r=upt |
| By: | Hernando Zuleta |
| Abstract: | We try to explain why economic conflicts and illegal business often take place in poor countries. We use the concept of subsistence level of consumption (d) and assume a regular concave utility function for consumption levels higher than d. For consumption levels lower than d utility is constant and equal to zero. Under this framework poor agents are risk-lovers. This result helps to explain why economic conflicts are more likely to appear in poor economies and why poor agents are more willing to undertake illegal business. |
| Date: | 2006–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:col:001070:002779&r=upt |
| By: | Jean-Philippe Lefort (CES - Centre d'économie de la Sorbonne - [CNRS : UMR8174] - [Université Panthéon-Sorbonne - Paris I]) |
| Abstract: | We adapt the model of comparisons of experts initiated by Lehrer («Comparison of experts JME 98») to a context of uncertainty which cannot be modelised by expected utility. We examine the robustness of Lehrer in this new context. Unlike expected utility, there exist several ways to define the strategies allowing to compare the experts, we propose some of them which guarantee a positive value of information. |
| Keywords: | Non-additive preferences, experts |
| Date: | 2007–02–12 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00130451_v1&r=upt |
| By: | George J. Bratsiotis; Baochun Peng |
| Abstract: | This paper examines how success-at-work, interpreted by both subjective and relative criteria, can motivate individuals to enhance their effort and utility. We employ a general specification utility function and show that the final effect of technological growth on individuals’ effort and utility depends, respectively, on the assumptions we make about their nature with regard to their effort strategies (i.e. conformists, deviants or neutrals) and to their utility preferences (i.e. altruistic or envious). We show that these effects are determined largely by individuals’ personal success-consciousness at-work, as well as their competition strategies towards relative success and status. |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:man:cgbcrp:86&r=upt |
| By: | Erick W. Rengifo (Department of Economics. Fordham University, New York); Emanuela Trifan (Institut für Volkswirtschaftslehre (Department of Economics), Technische Universität Darmstadt (Darmstadt University of Technology)) |
| Abstract: | This paper studies the impact of loss aversion on decisions regarding the allocation of wealth between risky and risk-free assets. We use a Value-at-Risk portfolio model with endogenous desired risk levels that are individually determined in an extended prospect theory framework. This framework allows for the distinction between gains and losses with respect to a subjective reference point as in the original prospect theory, but also for the influence of past performance on the current perception of the risky portfolio value. We show how the portfolio evaluation frequency impacts investor decisions and attitudes when facing financial losses and analyze the role of past gains and losses in the current wealth allocation. The perceived portfolio value exhibits distinct evolutions in two frequency segments delimitated by what we consider to be the optimal evaluation horizon of one year. Our empirical results suggest that previous research relying on fixed confidence portfolio risk levels underestimates the aversion of real individual investors to financial losses. |
| Keywords: | prospect theory, loss aversion, capital allocation, Value-at-Risk, portfolio evaluation |
| JEL: | C32 C35 G10 |
| Date: | 2007–02 |
| URL: | http://d.repec.org/n?u=RePEc:tud:ddpiec:180&r=upt |
| By: | Raphael A. Espinoza; Charles A. E. Goodhart; Dimitrios P. Tsomocos |
| Abstract: | We show, in an exchange economy with default, liquidity constraints and no aggregate uncertainty, that state prices in a complete markets general equilibrium are a function of the supply of liquidity by the Central Bank. Our model is derived along the lines of Dubey and Geanakoplos (1992). Two agents trade goods and nominal assets (Arrow-Debreu (AD) securities) to smooth consumption across periods and future states, in the presence of cashin-advance financing costs. We show that, with Von Neumann-Morgenstern logarithmic utility functions, the price of AD securities, are inversely related to liquidity. The upshot of our argument is that agents’ expectations computed using risk-neutral probabilities give more weight in the states with higher interest rates. This result cannot be found in a Lucas-type representative agent general equilibrium model where there is neither trade or money nor default. Hence, an upward yield curve can be supported in equilibrium, even though short-term interest rates are fairly stable. The risk-premium in the term structure is therefore a pure default risk premium. |
| Keywords: | cash-in-advance constraints; risk-neutral probabilities; state prices; term structure of interest rate |
| JEL: | E43 G12 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:sbs:wpsefe:2007fe01&r=upt |
| By: | Larry G. Epstein (University of Rochester) |
| Abstract: | Living with risk can lead to anticipatory feelings such as anxiety or hopefulness. Such feelings can a¤ect the choice between lotteries that will be played out in the future - choice may be motivated not only by the (static) risks involved but also by the desire to reduce anxiety or to promote savoring. This paper provides a model of preference in a three-period setting that is axiomatic and includes a role for anticipatory feelings. It is shown that the model of preference can accommodate intuitive patterns of demand for information such as information seeking when a favorable outcome is very likely and information aversion when it is more likely that the outcome will be unfavorable. Behavioral meaning is given to statements such as "individual 1 is anxious" and "2 is more anxious than 1". Finally, the model is di¤erentiated sharply from the classic model due to Kreps and Porteus. |
| Keywords: | risk, anxiety, savoring, anticipatory feelings, demand for commitment, demand for information, temporal resolution of risk, temptation |
| JEL: | D80 D81 |
| Date: | 2007–02 |
| URL: | http://d.repec.org/n?u=RePEc:roc:rocher:534&r=upt |
| By: | Nicholas Barberis; Ming Huang |
| Abstract: | We study the asset pricing implications of Tversky and Kahneman's (1992) cumulative prospect theory, with particular focus on its probability weighting component. Our main result, derived from a novel equilibrium with non-unique global optima, is that, in contrast to the prediction of a standard expected utility model, a security's own skewness can be priced: a positively skewed security can be "overpriced," and can earn a negative average excess return. Our results offer a unifying way of thinking about a number of seemingly unrelated financial phenomena, such as the low average return on IPOs, private equity, and distressed stocks; the diversification discount; the low valuation of certain equity stubs; the pricing of out-of-the-money options; and the lack of diversification in many household portfolios. |
| JEL: | D1 D8 G11 G12 |
| Date: | 2007–02 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:12936&r=upt |