2,023 research outputs found
Recursive Smooth Ambiguity Preferences.
No full textThis paper axiomatizes an intertemporal version of the Smooth Ambiguity decision model developed in [P. Klibanoff, M. Marinacci, S. Mukerji, A smooth model of decision making under ambiguity, Econometrica 73 (6) (2005) 1849–1892]. A key feature of the model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective beliefs, and ambiguity attitude, a characteristic of the decision maker's tastes. In applications one may thus specify/vary these two characteristics independent of each other, thereby facilitating richer comparative statics and modeling flexibility than possible under other models which accommodate ambiguity sensitive preferences. Another key feature is that the preferences are dynamically consistent and have a recursive representation. Therefore techniques of dynamic programming can be applied when using this model
The structure of variational preferences
No full textMaccheroni, Marinacci, and Rustichini (2006), in an Anscombe–Aumann framework, axiomatically characterize preferences that are represented by the variational utility functional V. In this paper, for a given variational preference, we study the class C of functions c that represent V. Inter alia, we show that this set is fully characterized by a minimal and a maximal element. The minimal element, also identified by Maccheroni, Marinacci, and Rustichini (2006), fully characterizes the decision maker’s attitude toward uncertainty, while the novel maximal element characterizes the uncertainty perceived by the decision maker
On the Smooth Ambiguity Model: A Reply
No full textWe …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 a¤ording a separation of ambiguity and ambiguity attitude or the potential for calibrating ambiguity attitude in the model
Dynamic variational preferences
No full textWe introduce and axiomatize dynamic variational preferences, the dynamic version of the variational preferences we axiomatized in [F. Maccheroni, M. Marinacci, A. Rustichini, Ambiguity aversion, robustness, and the variational representation of preferences, Mimeo, 2004], which generalize the multiple priors preferences of Gilboa and Schmeidler [Maxmin expected utility with a non-unique prior, J. Math. Econ. 18 (1989) 141–153], and include the Multiplier Preferences inspired by robust control and first used in macroeconomics by Hansen and Sargent (see [L.P. Hansen, T.J. Sargent, Robust control and model uncertainty, Amer. Econ. Rev. 91 (2001) 60–66]), as well as the classic Mean Variance Preferences of Markovitz and Tobin. We provide a condition that makes dynamic variational preferences time consistent, and their representation recursive. This gives them the analytical tractability needed in macroeconomic and financial applications. A corollary of our results is that Multiplier Preferences are time consistent, but MeanVariance Preferences are not
Ambiguity attitudes and self-confirming equilibrium in sequential games
No full textWe consider a game in extensive form recurrently played by agents who are randomly drawn from large populations and matched. We assume that preferences over actions at any information set admit a smooth-ambiguity representation in the sense of Klibanoff, Marinacci, and Mukerji (Econometrica, 2005), which may induce dynamic inconsistencies. We take this into account in our analysis of self-confirming equilibrium (SCE) given players' feedback about the path of play. Battigalli, Cerreia-Vioglio, Maccheroni, and Marinacci (Amer. Econ. Rev., 2015) show that the set of SCE's of a simultaneous-move game with feedback expands as ambiguity aversion increases. We show by example that SCE in a sequential game is not equivalent to SCE applied to the strategic form of such game, and that the previous monotonicity result does not extend to general sequential games. Still, we provide sufficient conditions under which the monotonicity result holds for SCE
A note on comparative ambiguity aversion and justifiability
No full textWe consider a decision maker who ranks actions according to the smooth ambiguity criterion of Klibanoff, Marinacci, and Mukerji (2005). An action is justifiable if it is a best reply to some belief over probabilistic models.We show that higher ambiguity aversion expands the set of justifiable actions. A similar result holds for risk aversion. Our results follow from a generalization of the duality lemma of Wald (1949) and Pearce (1984)
Model uncertainty
No full textWe study decision problems in which consequences of the various alternative actions depend on states determined by a generative mechanism representing some natural or social phenomenon. Model uncertainty arises because decision makers may not know this mechanism. Two types of uncertainty result, a state uncertainty within models and a model uncertainty across them. We discuss some two-stage static decision criteria proposed in the literature that address state uncertainty in the first stage and model uncertainty in the second (by considering subjective probabilities over models). We consider two approaches to the Ellsberg-type phenomena characteristic of such decision problems: a Bayesian approach based on the distinction between subjective attitudes toward the two kinds
of uncertainty; and a non-Bayesian approach that permits multiple subjective probabilities. Several applications are used to illustrate concepts as they are introduced
Necessary and sufficient conditions for optima in reflexive spaces
No full textWe give general necessary and sufficient conditions for the existence of optima of noncoercive functionals defined on reflexive spaces. Some special cases are then discussed that permit to establish novel sufficient conditions for optimality, as well as to recover known results
Decision analysis under ambiguity
No full textIn selecting the preferred course of action, decision makers are often uncertain about one or more probabilities of interest. The experimental literature has ascertained that this uncertainty (ambiguity) might affect decision makers’ preferences. Then, the decision maker might wish to incorporate ambiguity aversion in the analysis. We investigate the modeling ambiguity attitudes in the solution of decision analysis problems through functionals well-established in the decision theory literature. We obtain the multiple-event problems for subjective expected utility, smooth ambiguity and maximin decision makers. This allows us to establish the conditions under which these alternative decision makers face equivalent problems. Results for certainty equivalents and risk premia in the presence of both risk and ambiguity aversion are obtained. A recent generalization of the classical Arrow–Pratt quadratic approximation allows us to quantify the portions of a premium due to risk-, and to ambiguity-aversion. The numerical implementation of the objective functions is addressed, showing that all functionals can be estimated at no additional burden through Monte Carlo simulation. The well known Carter Racing case study is addressed quantitatively to demonstrate the findings
On concavity and supermodularity
No full textAbstractConcavity and supermodularity are in general independent properties. A class of functionals defined on a lattice cone of a Riesz space has the Choquet property when it is the case that its members are concave whenever they are supermodular. We show that for some important Riesz spaces both the class of positively homogeneous functionals and the class of translation invariant functionals have the Choquet property. We extend in this way the results of Choquet [G. Choquet, Theory of capacities, Ann. Inst. Fourier (Grenoble) 5 (1953–1954) 131–295] and König [H. König, The (sub/super) additivity assertion of Choquet, Studia Math. 157 (2003) 171–197]
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