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on Utility Models and Prospect Theory |
| By: | Tsogbadral Galaabaatar and Edi Karni, "Objective and Subjective Expected Utility with Incomplete Preferences", October 2010 |
| Abstract: | This paper extends the expected utility models of decision making under risk and under uncertainty to include incomplete beliefs and tastes. The main results are two axiomatizations of the multi-prior expected multi-utility representations of preference relation under uncertainty, thereby resolving long standing open questions. The Knightian uncertainty model and expected multi-utility model with complete beliefs are obtained as special cases. In addition, the von Neumann-Morgenstern expected utility model with incomplete preferences is revisited using a "constructive" approach, as opposed to earlier treatments that use convex analysis. |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:jhu:papers:572&r=upt |
| By: | David Roubaud; André Lapied; Robert Kast |
| Abstract: | Real options models characterized by the presence of “ambiguity” (or “Knightian uncertainty”) have been recently proposed. But based on recursive multiple-priors preferences, they typically describe ambiguity through a range of Geometric Brownian motions and solve it by application of a maxmin expected utility criterion among them (worst case). This reduces acceptable individual preferences to the single case of an extreme form of pessimism. In contrast, by relying on dynamically consistent “Choquet-Brownian” motions to represent the ambiguous cash flows expected from a project, we show that a much broader spectrum of attitudes towards ambiguity may be accounted for, improving the explanatory and application potentials of these appealing expanded real options models. In the case of a perpetual real option to invest, ambiguity aversion may delay the moment of exercise of the option, while the opposite holds true for an ambiguity seeking decision maker. Furthermore, an intricate relationship between risk and ambiguity appears strikingly in our model. |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:lam:wpaper:20-10&r=upt |
| By: | Peter Klibanoff; Massimo Marinacci; Sujoy Mukerji |
| Abstract: | We find that Epstein (2010)‘s Ellsberg-style thought experiments pose, contrary to his claims, no paradox or difficulty for the smooth ambiguity model of decision making under uncertainty developed by Klibanoff, Marinacci and Mukerji (2005). Not only are the thought experiments naturally handled by the smooth ambiguity model, but our reanalysis shows that they highlight some of its strengths compared to models such as the maxmin expected utility model (Gilboa and Schmeidler, 1989). In particular, these examples pose no challenge to the model’s foundations, interpretation of the model as affording a separation of ambiguity and ambiguity attitude or the potential for calibrating ambiguity attitude in the model. |
| Keywords: | Ambiguity, uncertainty, Knightian uncertainty, ambiguity aversion, uncertainty aversion, Ellsberg paradox, smooth ambiguity, smooth model, ambiguity hedging |
| JEL: | D80 D81 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:524&r=upt |
| By: | Susan K. Laury; Melayne Morgan McInnes; J. Todd Swarthout; Erica Von Nessen |
| Abstract: | We propose and test a new method for eliciting curvature-controlled discount rates that are invariant to the form of the utility function. The advantage of this method is that individual discount rates can be obtained without knowledge of risk attitude or parametric assumptions about the form of the utility function. We compare our single elicitation method that does not require estimation of the utility function to the Andersen et al. (2008) double elicitation technique in which the utility function and discount rates are jointly estimated. We use a laboratory experiment to perform a within-subjects comparison of discount rates from these two methods and find consistent results, which is reassuring given the wide range of estimates in the literature. In addition, the estimated discount rates in our study are "plausibly low" in contrast to the vast majority of other discount rate studies. Average discount rates are estimated to be between 12.2 and 14.1 percent. Our results are robust to relaxing the expected utility assumption of linearity in the probabilities, as we find little evidence of probability weighting in our data. |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:exc:wpaper:2011-01&r=upt |
| By: | Peter Klibanoff; Massimo Marinacci; Sujoy Mukerji |
| Abstract: | We examine a variety of preference-based definitions of ambiguous events in the context of the smooth ambiguity model. We first consider the definition proposed in Klibanoff, Marinacci, and Mukerji (2005) based on the classic Ellsberg two-urn paradox (Ellsberg (1961)), and show that it satisfies several desirable properties. We then compare this definition with those of Nehring (1999), Epstein and Zhang (2001), Zhang (2002) and Ghirardato and Marinacci (2002). Within the smooth ambiguity model, we show that Ghirardato and Marinacci (2002) would identify the same set of ambiguous and unambiguous events as our definition while Epstein and Zhang (2001) and Zhang (2002) would yield a different classification. Moreover, we discuss and formally identify two key sources of the differences compared to Epstein and Zhang (2001) and Zhang (2002). The more interesting source is that these two definitions can confound non-constant ambiguity attitude and the ambiguity of an event. |
| Keywords: | Ambiguity, uncertainty, Knightian uncertainty, ambiguity aversion, uncertainty aversion, Ellsberg paradox, |
| JEL: | D80 D81 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:525&r=upt |
| By: | A. M. G. Cox; David Hobson; Jan Obloj |
| Abstract: | We pursue an inverse approach to utility theory and consumption & investment problems. Instead of specifying an agent's utility function and deriving her actions, we assume we observe her actions (i.e. her consumption and investment strategies) and ask if it is possible to derive a utility function for which the observed behaviour is optimal. We work in continuous time both in a deterministic and stochastic setting. In a deterministic setup, we find that there are infinitely many utility functions generating a given consumption pattern. In the stochastic setting of the Black-Scholes complete market it turns out that the consumption and investment strategies have to satisfy a consistency condition (PDE) if they come from a classical utility maximisation problem. We further show that agent's important characteristics such as attitude towards risk (e.g. DARA) can be directly deduced from her consumption/investment choices. |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1101.3572&r=upt |
| By: | André Lapied; Robert Kast |
| Abstract: | In the real investments literature, the investigated cash flow is assumed to follow some known stochastic process (e.g. Brownian motion) and the criterion to decide between investments is the discounted utility of their cash flows. However, for most new investments the investor may be ambiguous about the representation of uncertainty. In order to take such ambiguity into account, we refer to a discounted Choquet expected utility in our model. In such a setting some problems are to dealt with: dynamical consistency, here it is obtained in a recursive model by a weakened version of the axiom. Mimicking the Brownian motion as the limit of a random walk for the investment payoff process, we describe the latter as a binomial tree with capacities instead of exact probabilities on its branches and show what are its properties at the limit. We show that most results in the real investments literature are tractable in this enlarged setting but leave more room to ambiguity as both the mean and the variance of the underlying stochastic process are modified in our ambiguous model. |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:lam:wpaper:21-10&r=upt |
| By: | Keita Owari |
| Abstract: | We study the convex duality method for robust utility maximization in the presence of a random endowment. When the underlying price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true for a wide class of utility functions on the whole real line and unbounded random endowment. To obtain this duality, we prove a robust version of Rockafellar's theorem on convex integral functionals and apply Fenchel's general duality theorem. |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1101.2968&r=upt |
| By: | Hryshko, Dmytro (University of Alberta, Department of Economics); Luengo-Prado, Maria Jose (Northeastern University); Sorensen, Bent (University of Houston) |
| Abstract: | We study the determinants of individual attitudes towards risk and,in particular,why some individuals exhibit extremely high risk aversion. Using data from the Panel Study of Income Dynamics we find that policy induced increases in high school graduation rates lead to significantly fewer individuals being highly risk averse in the next generation. Other significant determinants of risk aversion are age, sex, and parents' risk aversion. We verify that risk aversion matters for economic behavior in that it predicts individuals' volatility of income. |
| Keywords: | schooling reforms; risk attitudes; intergenerational persistence |
| JEL: | E21 I29 |
| Date: | 2011–01–01 |
| URL: | http://d.repec.org/n?u=RePEc:ris:albaec:2011_002&r=upt |
| By: | Edi Karni (Johns Hopkins University); Marie-Louise Vierø (Queen`s University) |
| Abstract: | This paper invokes the axiomatic approach to explore the notion of growing awareness in the context of decision making under uncertainty. It introduces a new approach to modeling the expanding universe of a decision maker in the wake of becoming aware of new consequences, new acts, and new links between acts and consequences. The expanding universe, or state space, is accompanied by extension of the set of acts. The preference relations over the expanded sets of acts are linked by unchanging preferences over the satisfaction of basic needs. The main results are representation theorems and corresponding rules for updating beliefs over expanding state spaces that have the flavor of “reverse Bayesianism.” |
| Keywords: | Awareness, unawareness, reverse Bayesianism |
| JEL: | D8 D81 D83 |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:qed:wpaper:1258&r=upt |
| By: | Ori Heffetz; John A. List |
| Abstract: | This paper is aimed to assess, with two lab experiments, to what extent Kőszegi and Rabin's (2006) model of expectations-based reference-dependent preferences can explain Knetsch's (1989) endowment effect. Departing from past work, we design an experiment that treats the two goods (a mug and a pen) symmetrically in all but in the probabilities with which they are expected to be owned. Thus, our "endowmentless" endowment effect experiment shuts down all alternative mechanisms while leaving expectations the only difference between treatments. We find no evidence that expectations alone can reproduce any of the original effect. |
| JEL: | C9 D11 Q26 |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:16715&r=upt |