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Abstract
Many results from expected utility theory still hold when the assumption of the existence of a utility function is replaced by the existence of local utility functions at each distribution. This dissertation contains three papers which extend the scope of generalized expected utility theory.
The first paper offers an interpretive comparison of the Arrow/Pratt and Ross characterizations of comparative risk aversion for expected utility maximizers. The tools used in this comparison are then applied to obtain a strengthening of the Ross characterization. This strengthened result is then extended to the case of smooth preferences over probability distributions.
In the second paper it is shown that local utility functions can be found under the weaker assumption of differentiable indifference manifolds. First order stochastic dominance preference, risk aversion, and comparative risk aversion are discussed using properties of the local utility functions.
In the third paper comparative statics results are discussed in the contexts of smooth preferences and preferences which have differentiable indifference surfaces. The existence of comparative statics derivatives is discussed. The comparative statics derivative which arises depends not only on the shapes of the local utility functions but also on how they change with changes in the defining wealth distribution. Examples of behavioral conditions which govern both aspects of this problem are given. Applications include the investor's portfolio choice problem and the competitive profit maximizing firm's output choice problem.
