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On the Smooth Ambiguity Model: A Reply
, 2009
"... Epstein (2009) describes three Ellsbergstyle thought experiments and argues that they pose di ¢ culties for the smooth ambiguity model of decision making under uncertainty developed by Klibano¤, Marinacci and Mukerji (2005). We revisit these thought experiments and
nd, to the contrary, that they ..."
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Epstein (2009) describes three Ellsbergstyle thought experiments and argues that they pose di ¢ culties for the smooth ambiguity model of decision making under uncertainty developed by Klibano¤, Marinacci and Mukerji (2005). We revisit these thought experiments and
nd, to the contrary, that they either point to strengths of the smooth ambiguity model compared to other models, such as the maxmin expected utility model (Gilboa and Schmeidler, 1989), or, in the case of one thought experiment, raise criticisms that apply equally to a broad range of current ambiguity models. 1
Relevance and Symmetry
, 2011
"... We de…ne a behavioral concept of relevance in the context of decision making under uncertainty. We argue that this concept provides a sensible answer to the question “What probabilistic environments do an individual’s preferences reveal as mattering to her decisions? ” under a symmetry assumption. T ..."
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We de…ne a behavioral concept of relevance in the context of decision making under uncertainty. We argue that this concept provides a sensible answer to the question “What probabilistic environments do an individual’s preferences reveal as mattering to her decisions? ” under a symmetry assumption. This question has important implications for economic modeling. It is often the case that a modeler desires to restrict the probabilistic environments a decision maker considers. Without a concept of relevant beliefs, it is impossible to check from preferences whether a model is re‡ecting what the modeler intended. This checking is essential to isolating the e¤ect of changing information while holding tastes …xed. We show that a single concept of relevance delivers this for a wide range of models, including models that allow for ambiguity attitude. We also use symmetry and relevance to provide insight into the foundations of theMEU and smooth ambiguity models of decisionmaking under uncertainty.
DISCUSSION PAPER SERIES ON THE SMOOTH AMBIGUITY MODEL: A REPLY
, 2011
"... We nd that Epstein (2010)s Ellsbergstyle thought experiments pose, contrary to his claims, no paradox or di ¢ culty for the smooth ambiguity model of decision making under uncertainty developed by Klibano¤, Marinacci and Mukerji (2005). Not only are the thought experiments naturally handled by the ..."
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We nd that Epstein (2010)s Ellsbergstyle thought experiments pose, contrary to his claims, no paradox or di ¢ culty for the smooth ambiguity model of decision making under uncertainty developed by Klibano¤, 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 models foundations, interpretation of the model as a¤ording a separation of ambiguity and ambiguity attitude or the potential for calibrating ambiguity attitude in the model. JEL Classi
cation Numbers: D800, D810.
ScienceDirect Subjective independence and concave expected utility
"... Abstract When a potential hedge between alternatives does not reduce the exposure to uncertainty, we say that the decision maker considers these alternatives structurally similar. We offer a novel approach and suggest that structural similarity is subjective and should be different across decision ..."
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Abstract When a potential hedge between alternatives does not reduce the exposure to uncertainty, we say that the decision maker considers these alternatives structurally similar. We offer a novel approach and suggest that structural similarity is subjective and should be different across decision makers. Structural similarity can be recovered through a property of the individual's preferences referred to as subjective codecomposable independence. This property characterizes a class of eventseparable models and allows us to differentiate between perception of uncertainty and attitude towards it. In addition, our approach provides a behavioral foundation to Concave Expected Utility preferences.
The opinions expressed in the working papers are those of the authors alone, and not those of the Institute, which takes non institutional policy position, nor those of CEPR, NBER or Università Bocconi. On the Smooth Ambiguity Model: A Reply ∗
"... We find that Epstein (2010)’s Ellsbergstyle thought experiments pose, contrary to his claims, no paradox or diffi culty 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 ..."
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We find that Epstein (2010)’s Ellsbergstyle thought experiments pose, contrary to his claims, no paradox or diffi culty 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. 1
Relevance and Symmetry ∗
, 2012
"... This paper provides a method to identify components of preference reflecting information and those reflecting only tastes. Important to this method is the identification of a unique set of revealed probability assignments (called relevant measures) from preferences over acts. We characterize these r ..."
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This paper provides a method to identify components of preference reflecting information and those reflecting only tastes. Important to this method is the identification of a unique set of revealed probability assignments (called relevant measures) from preferences over acts. We characterize these relevant measures and show where they appear in representations of preferences. This method works for a large set of preference models provided that the state space is treated as if it had a symmetric, “i.i.d. with unknown parameters, ” structure. Relevant measures are shown to characterize revealed information and to help in identifying taste components of preference representations. We apply our findings to four wellknown representations of ambiguitysensitive preferences: the αMEU model, the smooth ambiguity model, the extended MEU with contraction model and the vector expected utility model. For each representation, the theory identifies both the set of relevant measures and components of the representation that reflect only tastes.
Machina’s Reflection Example and VEU Preferences: a Very Short Note
, 2008
"... Machina [8] proposes examples of plausible preference patterns that cannot be accommodated by the Choquet expected utility model (Schmeidler [9]). In a recent paper, Baillon, L’Haridon and Placido [2] show that Machina’s examples also pose a challenge for other popular models, including maxmin expec ..."
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Machina [8] proposes examples of plausible preference patterns that cannot be accommodated by the Choquet expected utility model (Schmeidler [9]). In a recent paper, Baillon, L’Haridon and Placido [2] show that Machina’s examples also pose a challenge for other popular models, including maxmin expected utility (Gilboa and Schmeidler [5]), variational preferences (Maccheroni, Marinacci and Rustichini [7]) and the “smooth ambiguity model ” of Klibanoff, Marinacci and Mukerji [6]. This note focuses on the “reflection example, ” reproduced in Section 2 below; it argues that Machina’s reflection example highlights important behavioral differences between notions of ambiguity aversion that are either implied by, or natural, in a variety of decision models. I adopt the vector expected utility (henceforth VEU) model of Siniscalchi [10]. This is useful in the present context because VEU preferences admit a relatively “structured ” representation,
and
, 2009
"... We introduce and analyze expected uncertain utility theory (EUU). Apriorandan interval utility characterize an EUU decision maker. The decision maker uses her subjective prior to transform each uncertain prospect f into an intervalvalued prospect f which assigns an interval [x, y] of prizes to each ..."
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We introduce and analyze expected uncertain utility theory (EUU). Apriorandan interval utility characterize an EUU decision maker. The decision maker uses her subjective prior to transform each uncertain prospect f into an intervalvalued prospect f which assigns an interval [x, y] of prizes to each state. The decision maker ranks prospects according to their expected interval utilities E(u(f)) where u is the index that specifies the utility of each interval [x, y]. We define risk and ambiguity aversion for EUU, use the EUU model address the Allais Paradox, the Ellsberg Paradox, the Home Bias and relate these behaviors to the individuals attitude towards risk and ambiguity. We introduce and analyze expected uncertain utility theory (EUU), a model of decision making under uncertainty. The choice objects are Savage acts that associate a monetary prize to every state of nature. The goal is to provide a theory that can address three
Partial Ambiguity
, 2013
"... This paper investigates attitude towards partial ambiguity. In a laboratory setting, we study three symmetric variants of the ambiguous urn in Ellsberg’s 2urn paradox by varying the possible compositions of red and black cards in a 100card deck. Subjects value betting on a deck with a smaller set ..."
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This paper investigates attitude towards partial ambiguity. In a laboratory setting, we study three symmetric variants of the ambiguous urn in Ellsberg’s 2urn paradox by varying the possible compositions of red and black cards in a 100card deck. Subjects value betting on a deck with a smaller set of possible compositions more, even when they share the same end points. The valuation of lotteries with only two possible compositions decreases in the degree of spread except for a reversal when it approaches the extreme case of either all red or all black. We further study attitude towards skewed ambiguity and …nd that subjects tend to switch from being ambiguity averse to ambiguity tolerant as the degree of skewness increases. This paper also discusses the implications of our …ndings for existing models of decision making under uncertainty including those based on multiple priors, a twostage perspective, and source preference.
Brisbane
, 2011
"... A twoparameter model of dispersion aversion. The idea of representing choice under uncertainty as a tradeoff between mean returns and some measure of risk or uncertainty is fundamental to the analysis of investment decisions. In this paper, we show that preferences can be characterized in this way ..."
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A twoparameter model of dispersion aversion. The idea of representing choice under uncertainty as a tradeoff between mean returns and some measure of risk or uncertainty is fundamental to the analysis of investment decisions. In this paper, we show that preferences can be characterized in this way, even in the absence of objective probabilities. We develop a model of uncertainty averse preferences that is based on a mean and a measure of the dispersion of the statewise utility of an act. The dispersion measure exhibits positive linear homogeneity, subadditivity, translation invariance and complementary symmetry. Since preferences are only weakly separable in terms of these two summary statistics, the uncertainty premium need not be constant. We show that the standard results originally derived in the context of meanvariance analysis and expected utility theory apply in this more generally setting. In particular, we generalize the concept of decreasing absolute risk aversion and show that the usual comparative static results from EU theory remain valid. Further we derive twofund separation and asset pricing results analogous to those that hold for the standard CAPM.