Updating preferences with multiple priors

We propose and axiomatically characterize dynamically consistent update rules for decision making under ambiguity. These rules apply to the preferences with multiple priors of Gilboa and Schmeidler (1989), and are the first, for any model of preferences over acts, to be able to reconcile typical behavior in the face of ambiguity (as exemplified by Ellsberg’s paradox) with dynamic consistency for all non-null events. Updating takes the form of applying Bayes’ rule to subsets of the set of priors, where the specific subset depends on the preferences, the conditioning event, and the choice problem (i.e., a feasible set of acts together with an act chosen from that set).Updating, dynamic consistency, ambiguity, Ellsberg, Bayesian, consequentialism

Updating Ambiguity Averse Preferences

Dynamic consistency leads to Bayesian updating under expected utility. We ask what it implies for the updating of more general preferences. In this paper, we charac- terize dynamically consistent update rules for preference models satisfying ambiguity aversion. This characterization extends to regret-based models as well. As an appli- cation of our general result, we characterize dynamically consistent updating for two important models of ambiguity averse preferences: the ambiguity averse smooth am- biguity preferences (Klibanoff, Marinacci and Mukerji [Econometrica 73 2005, pp. 1849-1892]) and the variational preferences (Maccheroni, Marinacci and Rustichini [Econometrica 74 2006, pp. 1447-1498]). The latter includes max-min expected utility (Gilboa and Schmeidler [Journal of Mathematical Economics 18 1989, pp. 141-153]) and the multiplier preferences of Hansen and Sargent [American Economic Review 91(2) 2001, pp. 60-66] as special cases. For smooth ambiguity preferences, we also identify a simple rule that is shown to be the unique dynamically consistent rule among a large class of rules that may be expressed as reweightings of Bayes's rule.Updating, Dynamic Consistency, Ambiguity, Regret, Ellsberg, Bayesian, Consequentialism, Smooth Ambiguity

A smooth model of decision making under ambiguity.

We propose and axiomatize a new model of preferences that achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective information, and ambiguity attitude, a characteristic of the decision maker's tastes.Ambiguity; Uncertainty; Knightian Uncertainty; Ambiguity Aversion; Uncertainty Aversion; Ellsberg Paradox

Recursive Smooth Ambiguity Preferences

This paper axiomatizes an intertemporal version of the Smooth Ambiguity decision model developed in Klibanoff, Marinacci, and Mukerji (2005). 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 accomodate 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.Ambiguity, Uncertainty, Knightian Uncertainty, Ambiguity Aversion, Uncertainty Aversion, Ellsberg Paradox, Dynamic Decision Making, Dynamic Programming under Ambiguity, Smooth Ambiguity.

Linearity with Multiple Priors

We characterize the types of functions over which the functional defined as the "min" of integrals with respect to probabilities in a given non-empty closed and convex class is linear. This happens exactly when "integrating" functions which are positive affine transformations of each other (or when one is constant). We show that the result is quite general by restricting the types of classes of probabilities considered. Finally we prove that, with a very peculiar exception, all the results hold more generally for functionals which are linear combinations of the "min" and the "max" functional

Subjective recursive expected utility

We axiomatize a subjective version of the recursive expected utility model. This development extends the seminal results of Kreps and Porteus (Econometrica 46:185–200 (1978)) to a subjective framework and provides foundations that are easy to relate to axioms familiar from timeless models of decision making under uncertainty. Our analysis also clarifies what is needed in going from a represention that applies within a single filtration to an across filtration representation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45855/1/199_2005_Article_41.pd

Investment under ambiguity with the best and worst in mind

Recent literature on optimal investment has stressed the difference between the impact of risk and the impact of ambiguity - also called Knightian uncertainty - on investors' decisions. In this paper, we show that a decision maker's attitude towards ambiguity is similarly crucial for investment decisions. We capture the investor's individual ambiguity attitude by applying alpha-MEU preferences to a standard investment problem. We show that the presence of ambiguity often leads to an increase in the subjective project value, and entrepreneurs are more eager to invest. Thereby, our investment model helps to explain differences in investment behavior in situations which are objectively identical

A dynamic mechanism and surplus extraction under ambiguity

We study the question of auction design in an IPV setting characterized by ambiguity. We assume that the preferences of agents exhibit ambiguity aversion; in particular, they are represented by the epsilon-contamination model. We show that a simple variation of a discrete Dutch auction can extract almost all surplus. This contrasts with optimal auctions under IPV without ambiguity as well as with optimal static auctions with ambiguity—in all of these, types other than the lowest participating type obtain a positive surplus. An important point of departure is that the modified Dutch mechanism is dynamic rather than static, establishing that under ambiguity aversion—even when the setting is IPV in all other respects—a dynamic mechanism can have additional bite over its static counterparts. A further general insight is that the standard revelation principle does not automatically extend to environments not characterized by subjective expected utility

Investor Reaction to Salient News in Closed-End Country Funds

We provide a model of closed-end fund pricing which includes investors who do not form expectations correctly and allows for salient country-specific news to affect this expectation formation process. We use panel data on prices and net asset values of closed- end country funds to examine investor reaction to news that affects fundamentals, and measure the response of the idiosyncratic change in fund prices to the idiosyncratic change in fund asset values. In a typical week, US prices underreact to changes in foreign fundamentals; the (short-run) elasticity of price with respect to asset value is significantly less than one. In weeks with major news (relevant to the specific country) appearing on the front page of The New York Times, prices react much more to fundamentals; the elasticity of price with respect to asset value is closer to one. These results are roughly consistent with the hypothesis that major news events lead some investors who normally lag behind in updating their expectations to temporarily react more quickly.