Financial decision-making under distribution uncertainty.

Abstract

Investors do not know the distribution of future returns, but much of the finance literature assumes they do. This dissertation presents a novel approach which allows one to incorporate uncertainty about the type of return distribution (distribution uncertainty) and applies it to three different financial problems: asset allocation, return predictability, and option pricing. To analyze decisions under distribution uncertainty, I develop a new family of Bayesian nonparametric and semiparametric models. In such models, the nonparametric component is modeled using the class of Dirichlet processes, while the parametric component is modeled using mean-variance regression. I show that, in such a semiparametric framework, the predictive distribution for any decision variable can be obtained using a scale mixture of uniform distributions approach. Importantly, such predictive distribution accounts for both parameter- and distribution uncertainty. I find that, above and beyond parameter uncertainty, distribution uncertainty is highly time-varying. Compared to investors facing a standard parameter uncertainty, investors considered in this dissertation can benefit from accounting for distribution uncertainty when deciding about optimal asset allocation, or predicting option prices. Distribution uncertainty, however, does not help to improve a well-known weak evidence on short-term predictability from the dividend yield.