We provide conditions under which contingent claim and asset demands are consistent with state independent Expected Utility maximization. The paper focuses on the case of a single commodity and demands are allowed to be functions of probabilities and not just prices and income. We extend prior analyses by deriving three distinct tests for demands to be rationalized by Expected Utility: (i) a contingent claim analogue to the certainty strong axiom of revealed preference, (ii) a characterization of the functional form for demand, and (iii) necessary and sufficient conditions based on the Slutsky matrix.

The standard assumption that asset demand increases in income and decreases in price has its origin in Arrow's classic model with one risky and one risk free asset, where both are held long, and preferences exhibit decreasing absolute and increasing relative risk aversion. However if one allows shorting of the risk free asset or decreasing relative risk aversion, the risk free asset can not only fail to be a normal good but can be a Giffen good. This behavior can occur even for members of the popular HARA utility family. More generally, Giffen behavior can occur over multiple income ranges.