Foundations Of Statistics

Recursive multiple-priors

We often deal with uncertain events for which no probabilities are known. Several normative models have been proposed. Descriptive studies have usually been qualitative, or they estimated ambiguity aversion through one single number. This paper introduces the source method, a tractable method for quantitatively analyzing uncertainty empirically. The theoretical key is the distinction between different sources of uncertainty, within which subjective (choice-based) probabilities can still be defined. Source functions convert those subjective probabilities into willingness to bet. We apply our method in an experiment, where we do not commit to particular ambiguity attitudes but let the data speak.

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The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation

This book describes the classical axiomatic theories of decision under uncertainty, as well as critiques thereof and alternative theories. It focuses on the meaning of probability, discussing some definitions and surveying their scope of applicability. The behavioral definition of subjective probability serves as a way to present the classical theories, culminating in Savage's theorem. The limitations of this result as a definition of probability lead to two directions - first, similar behavioral definitions of more general theories, such as non-additive probabilities and multiple priors, and second, cognitive derivations based on case-based techniques.

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Theory of decision under uncertainty

A sequentially rationalizable choice function is a choice function that can be retrieved by applying sequentially to each choice problem the same xed set of asymmetric binary relations (rationales) to remove inferior alternatives. These con- cepts translate into economic language some human choice heuristics studied in psychology and explain cyclical patterns of choice observed in experiments. We study some properties of sequential rationalizability and provide a full character- ization of choice functions rationalizable by two and three rationales.

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Sequentially Rationalizable Choice

http://eurequa.univ-paris1.fr/membres/vergnaud/GHTV-finalJET.pdf

Attitude toward imprecise information

http://static.luiss.it/hey/ambiguity/papers/Hayashi_2008.pdf

Regret aversion and opportunity dependence

In this paper, we establish an axiomatically founded generalized recursive smooth ambiguity model that allows for a separation among intertemporal substitution, risk aversion, and ambiguity aversion. We axiomatize this model using two approaches: the second-order act approach a la Klibanoff et al. (2005) and the twostage randomization approach a la Seo (2009). We characterize risk attitude and ambiguity attitude within these two approaches. We then discuss our model’s application in asset pricing. Our recursive preference model nests some popular models in the literature as special cases.

/pdf/intertemporal-substitution-and-recursive-smooth-ambiguity-ngshcmdxyk.pdf

Intertemporal substitution and recursive smooth ambiguity preferences

This article provides an experimental analysis of attitude toward imprecise and variable information. Imprecise information is provided in the form of a set of possible probability values, such that it is virtually impossible for the subjects to guess or estimate, which one in the set is true or more likely to be true. We investigate how geometric features of such information pieces affect choices. We find that the subjects care about more features than the pairs of best-case and worst-case, which is a counter-evidence to the well-known models, maximin and α-maximin. We find that presence of nonextreme points in the set affects choice, which suggests that attitude toward imprecision is ‘nonlinear.’ We also obtain an observation, though not significant, that information pieces have a complementarity that may not be explained by the Bayesian view.

Choice with imprecise information: an experimental approach

This paper axiomatizes a form of recursive utility on consumption processes that permits a role for ambiguity as well as risk. The model has two prominent special cases: (i) the recursive model of risk preference due to Kreps and Porteus [18]; and (ii) an intertemporal version of multiple-priors utility due to Epstein and Schneider [8]. The generalization presented here permits a three-way separation of intertemporal substitution, risk aversion and ambiguity aversion.

https://pages.stern.nyu.edu/~dbackus/Exotic/1Ambiguity/Hayashi%20EZ%20Dec%2003.pdf

Takashi Hayashi

Papers

Attitude toward imprecise information

Regret aversion and opportunity dependence

Intertemporal substitution and recursive smooth ambiguity preferences

Choice with imprecise information: an experimental approach

Intertemporal substitution, risk aversion and ambiguity aversion*