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Thomas Knox
Business Economics PhD

Dissertation Chair: Prof. G. Chamberlain

Learning How to Invest When Returns Are Uncertain

Most asset returns are uncertain, not merely risky: investors do not know the probabilities of different future returns. A large body of evidence suggests that investors are averse to uncertainty, as well as to risk. This dissertation analyzes the dynamic portfolio and consumption choices of an uncertainty-averse (as well as risk-averse) investor who tries to learn from historical data.

In the first chapter of this dissertation, ''Foundations for Learning How to Invest when Returns are Uncertain,'' I build up a general theory of dynamic choice under uncertainty aversion, based on the maxmin expected utility theory of Gilboa and Schmeidler (1989), from axioms on preferences. I pay special attention to the existence and consistency of conditional preferences. My theory, "model-based multiple-priors,'' generalizes one of the leading uncertainty-aversion theories in the literature (recursive multiple-priors) by relaxing the assumption of consequentialism. I give examples to show that consequentialism, the property that counterfactuals are ignored, can be problematic when combined with uncertainty aversion. Model-based multiple-priors avoids the problems that enforcing consequentialism may create. In the context of a simple portfolio choice problem, I compare the leading approaches to uncertainty aversion in asset pricing with each other and with model-based multiple-priors. The model-based multiple-priors theory leads naturally to learning.

''Analytical Methods for Learning How to Invest when Returns are Uncertain,'' the second chapter of this dissertation, presents closed-form solutions to several continuous-time portfolio and consumption choice problems uncertainty-averse investors might face. First, I consider the case of a single risky (and uncertain) asset; next, I analyze the multiple-asset case; finally, I apply the multiple-asset theory to study learning about an uncertain asset pricing model.

The third and final chapter of this dissertation, ''Numerical Methods for Learning How to Invest when Returns are Uncertain,'' considers the numerical solutions of two consumption and portfolio choice problems which seem to be analytically intractable. First, the single-uncertain-asset case considered in the second chapter is generalized by allowing for less restricted forms of uncertainty. This necessitates numerical approaches, which reveal some nuances of the problem that were not evident under more restricted forms of uncertainty. Second, I analyze learning about uncertain return predictability. In order to do so, I shift to a discrete-time setting in which the investor makes a one-period portfolio choice after observing a quantity of data relevant to the uncertain predictability of returns.

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