Date of Award
Doctor of Philosophy (PhD)
Over the past two decades, the growing literature on ambiguity aversion has shed light on a number of puzzles in financial economics. In most applications, however, a learning mechanism that maps observations to a posteriori ambiguity is absent. Instead, a form of ambiguity known as IID ambiguity that is to model agents after they have learned all that they can has been the dominant specification in the literature. But when do we have the conjectured IID ambiguity? When does ambiguity resolve and when does it not? When it persists, what determines its long-run level and what are reasonable variations? In this dissertation, I provide answers to these questions by proposing a model of learning under ambiguity and investigate their implications for portfolio choice and asset pricing.
Specifically, I focus on the Gilboa-Schmeidler (1989) ambiguity aversion and assume that agents have the Chen-Epstein (2002) continuous-time recursive multiple-priors utility. Then, a learning mechanism means a map from each time-state to a set of one-step-ahead conditionals. I assume that the agents' beliefs about the data-generating mechanism are represented by multiple probabilistic models. As data accumulate, they assess the likelihood of each model, discard the ones with low likelihood, and update the remaining ones by Bayes' rule model-by-model. The dynamics of learning is explicitly characterized in the form of a system of differential equations and I observe that in revising their estimates, agents take into account both the uncertainty within each model and the uncertainty over the models. An application to portfolio choice shows that the effect of learning under ambiguity can be significant; the optimal weight on stocks monotonically decreases as the investor loses confidence and the decrease can be as large as 50\% of wealth. Finally, in an application to asset pricing, I make three observations regarding the equilibrium equity premium. First, learning under ambiguity generates a declining trend in the equity premium. Second, an improvement in the quality of signals can result in a higher equity premium. Third, the relationship between the equity premium and the conditional variance of returns is uncertain; they may be negatively correlated.
Choi, Hongseok, "Essays on Learning Under Ambiguity" (2012). Publicly Accessible Penn Dissertations. 3216.