Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/81101
Authors: 
Dumav, Martin
Stinchcombe, Maxwell B.
Year of Publication: 
2013
Series/Report no.: 
Working Papers, Center of Mathematical Economics 480
Abstract: 
A choice problem is risky (respectively ambiguous) if the decision maker is choosing between probability distributions (respectively sets of probability distributions) over utility relevant consequences. We provide an axiomatic foundation for and a representation of continuous linear preferences over sets of probabilities on consequences. The representation theory delivers: rst and second order dominance for ambiguous problems; a utility interval based dominance relation that distinguishes between sources of uncertainty; a complete theory of updating convex sets of priors; a Bayesian theory of the value of ambiguous information structures; complete separations of attitudes toward risk and ambiguity; and new classes of preferences that allow decreasing relative ambiguity aversion and thereby rationalize recent challenges to many of the extant multiple prior models of ambiguity aversion. We also characterize a property of sets of priors, descriptive completeness, that resolves several open problems and allows multiple prior models to model as large a class of problems as the continuous linear preferences presented here.
Subjects: 
Ambiguity
decision theory
multiple priors
descriptive completeness
continuous linear functionals on spaces of sets
constant and decreasing relative ambiguity aversion
zonoids
Document Type: 
Working Paper

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