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: This paper develops tools for analyzing properties of stochastic objective functions that take the form (,)(,)(;) VudF s xxssqqqq. The paper analyzes the relationship between properties of the primitive functions, such as the utility functions u and probability distributions F, and properties of the stochastic objective. The methods are designed to address problems where the utility function is restricted to lie in a set of functions which is a "closed convex cone" (examples of such sets include increasing functions, concave functions, or supermodular functions). It is shown that approaches previously applied to characterize monotonicity of V (that is, stochastic dominance theorems) can be used to establish other properties of V as well. The first part of the paper establishes necessary and sufficient conditions for V to satisfy "closed convex cone properties" such as monotonicity, supermodularity, and concavity, in the parameter q q. Then, we consider necessary and suf...
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