Essays on subjective probability, risk and ambiguity

This thesis focuses on foundations for the use of subjective probability in decision making and for the subjective distinction between risk and ambiguity.;In the first chapter, I generalize the theory of subjective expected utility due to Savage and the theory of probabilistic sophistication due to Machina-Schmeidler. The axioms used by these authors are relaxed in order to accommodate ambiguity, that is, the decision maker's unwillingness to assign subjective probabilities to some events as illustrated by the Ellsberg Paradox. The two main results---one for expected utility, the other for probabilistic sophistication---derive subjective probabilities but only for risky events. The distinction between risky and ambiguous events can be defined in terms of preference. In this way, one can obtain a fully subjective theory of expected utility and a fully subjective theory of probabilistic sophistication. In both cases, the values and the domain of the decision maker's probabilistic belief are derived from her preference. The analysis identifies a mathematical structure---called a mosaic---that is appropriate for the domain of subjective probability. In contrast with an algebra or a sigma-algebra, this structure is implied by the subjective definitions of risky events. The construction of probability on a mosaic of risky events is based on an explicit formula that captures a simple intuition and is free of some of the limitations of Savage's approach.;In the second chapter, I present a cognitive procedure that the decision maker may use to extend her preference from a subdomain of risky prospects ranked via expected utility to the universal domain of all uncertain prospects. This procedure reflects a form of partial ignorance and delivers a preference ordering that can be represented by alpha-maxmin expected utility, that is, a weighted sum of maxmin and maximax expected utilities. The unique weight alpha is interpretable as an index of ambiguity attitude; it ranges from aversion (alpha = 1) to affinity (alpha = 0).