Measurements and forecasting of risk involve distributional assumptions of the determinants of the model. Financial time series are often modeled as autoregressive integrated moving averages, which assumes the researcher requires only the data series to develop effective forecasts of returns, and to price risky assets. Insurance companies, investment banking institutions, commercial banks, and consumers vested in portfolios of risky assets can earn extraordinary returns when they can accurately assess the unrevealed value of an asset. Economists prefer to assess risk using consumption-based pricing models. Paramount in economic theory is the utility-maximizing agent, consuming in the market subject to production or budget constraints.; The theoretical constructs of certain well-known models have been criticized due to several paradoxes that question the empirical viability of the models. In particular, expected utility functions that conform to the von Neumann-Morgenstern axioms have not forecast consumer behavior very accurately in a series of questionnaires where consumers are asked to reveal their preferences about certain lotteries. These systematic violations of the von Neumann-Morgenstern expected utility functionals are known as the Allais paradox. Another paradox, not as well known as the Allais paradox, is the Ellsberg paradox. The Ellsberg paradox appears to involve systematic violations of subjective probability measures. Related to these is a shortcoming of the Lucas one-tree model for pricing assets: the equity premium puzzle, which amounts to an additional paradox. All three paradoxes are resolved in this dissertation. They are resolved by judicious modification of the assumptions in the model. These modifications in theory provide insights into pricing assets with uncertain returns. As a result, the expected utility function emerges almost intact, and the modifications add to the robustness of consumption-based asset pricing theory for forecasting consumer behavior.
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