In this dissertation, I examine the impact of uncertainty and information processing restrictions on standard economic models. Chapter 1 examines a reevaluation of the excess volatility puzzle in asset prices by assessing the impact of a shift in the agent's focus from minimizing average loss to minimizing maximum loss. Chapters 2 and 3 extend and clarify the newly developing arena of economic models in which the agent's capacity for information processing is systematically limited, as in the recent rational inattention literature. Chapter 1, which represents joint work with Charles Whiteman, studies the consequences changing the present value formula for stock prices. In place of the squared-error-loss minimizing expected present value of future dividends, we use a predictor optimal for the min-max preference relationship appropriate in cases of ambiguity. With ``robust" predictions, the well-known variance bound is reversed in that prices are predicted to be far more volatile than what is observed. We also investigate an intermediate ``partially robust'' case in which the degree of ambiguity is limited, and discover that such an intermediate model cannot be rejected in favor of an unrestricted time series model. Chapter 2 demonstrates the properties and solutions for the more general two-period rational inattention model. We show that the problem is convex, can be solved in seconds, and highlights several important features of information-processing-capacity-constrained models. Additionally, we show the importance of deriving, rather than assuming, the form of the final solution in rational inattention models. Chapter 3 extends the work of Chapter 2 to a finite-horizon dynamic setting by creating a structure in which distributional state and control variables interact under information-processing constraints. Limited information processing capacity is used optimally, and agents have the opportunity to trade processing capacity for higher expected future income. The framework is applied to the canonical life-cycle model of consumption and saving, and an analysis of the impact of preference parameters on optimal attention allocation is conducted. The model produces a distinct hump-shaped profile in expected consumption.