Analytical Methods for 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 paper uses the model-based multiple-priors framework developed in Knox (2003) to analyze the dynamic portfolio and consumption choices of an uncertainty-averse (as well as risk-averse) investor who tries to learn from historical data. Closedform solutions are given for several continuous-time portfolio and consumption choice problems that uncertainty-averse investors might face. First, the case of a single risky (and uncertain) asset is considered; next, the multiple-asset case is analyzed; finally, the multiple-asset theory is applied to study learning about an uncertain asset pricing model. ∗This paper is a revision of the second chapter of my doctoral thesis; I am indebted to Gary Chamberlain and John Campbell for guidance and encouragement throughout the writing of my thesis. I am also grateful for the insights of Brian Hall, Lars Hansen, Parag Pathak, Jacob Sagi, Tom Sargent, Jeremy Stein, and James Stock, and for the helpful comments of seminar participants at the University of California, Berkeley, the University of Chicago Graduate School of Business, the Fuqua School of Business at Duke University, Harvard Business School, Harvard University, the Kellogg School of Management at Northwestern University, New York University Stern School of Business, Princeton University, and the Wharton School of the University of Pennsylvania. I am solely responsible for the remaining shortcomings of this paper. 1