Hening Liu

Publication Date


Document Type


First Advisor

Anderson, Evan W.

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Economics


Individual investors--Psychology; Investments--Mathematical models


This dissertation examines dynamic portfolio and consumption decisions in continuous time for an ambiguity-averse investor when investment opportunities are time varying and stochastic. The investor doubts the estimated model for investment opportunities. Further, the investor has a set of priors and is ambiguous about which model in the set of priors is the true data-generating process. The optimal portfolio and consumption decisions with ambiguity aversion can be explicitly solved by the martingale method. This research considers two types of time varying investment opportunities: unobservable regime switching mean returns and mean-reverting returns. In the first case, the optimal portfolio can be explicitly characterized using a variational stochastic calculus technique, which is known as the Malliavin calculus. Estimation risk and ambiguity are shown to have opposite effects on the optimal hedging portfolio. Ambiguity can make the optimal portfolio depend on the investment horizon in a non-monotonic way. Further, ambiguity can reduce the welfare gain from learning. In the second case, the optimal portfolio and consumption decision rules can be solved in closed form in complete markets. Ambiguity is shown to have effects on the myopic portfolio, the hedging portfolio, and the consumption-wealth ratio.


Includes bibliographical references (pages [74]-78).


vi, 83 pages




Northern Illinois University

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