Risk, Ambiguity and Dynamic Choice

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This project studies two different problems in decision making under uncertainty. The first deals with the resolution of uncertainty over time. The choices that individuals make reflect not only their concern for the uncertain ultimate outcome but also their interest in how this uncertainty will resolve over time. We develop a new model of preference for temporal resolution of uncertainty that is simpler than existing models, closer to many standard dynamic models of economics and finance and, therefore, requires less data on individuals' beliefs about the future. Our second projects deals with ambiguity; that is, situations in which individuals find it difficult to quantify the uncertainty they are confronting. We propose a framework in which decision makers distinguish between unambiguous and ambiguous events and use the former to calibrate the latter. Thus, each unambiguous event, A, is calibrated by two events, the least likely unambiguous event more likely than A and the most likely unambiguous event less likely than A. Our goal is to develop a subjective (i.e., preference-based) theory of uncertainty that permits ambiguity perception and yet is amenable to suitably modified versions of probability theory and statistics. Models of temporal resolution of uncertainty and models of ambiguity both have many applications in macroeconomics and finance. Both of these lines of inquiry are limited by difficulties in developing and testing models. Our simpler models should facilitate these applications and make it easier to identify their parameters and find the relevant empirical evidence.Our model of temporal resolution of uncertainty differs from the Kreps and Porteus' model by allowing for preference for early resolution without requiring sensitivity to higher order information that does not affect fundamentals; it is analogous to standard dynamic models of choice without preference for timing of resolution. In such models, the decision maker derives utility each period from her possibly random consumption in that period. In our model, the decision maker derives utility only from her beliefs about what she will ultimately consume, not from her beliefs about how her beliefs will evolve. This part of the research has the following goals: (i) provide an axiomatic foundation of risk consumption preferences. (ii) Develop and analyze appropriate measures of preference for early/late resolution of uncertainty. (iii) Investigate the implications of risk consumption preferences in various applications. Our model of calibrated ambiguity offers a new notion ambiguity perception (which we call qualitative uncertainty relations). Our main result establishes an inner probability representation for qualitative uncertainty analogous to the Dempster-Shafer theory. To be able to distinguish ambiguity perception from ambiguity attitude, we allow the qualitative uncertainty relation to be incomplete. This incompleteness reflects the fact that when there is ambiguity, a decision maker's perception of ambiguity by itself, is not sufficient to determine her ranking of bets. The goal of this research is to provide a representation theorem for qualitative uncertainty relations and use it to study updating, inference and the relationships among existing models of ambiguity and evidence.