Continuous-Time and Distributionally Robust Mean-Variance Models

This thesis contains three works in both continuous-time and distributionally robust mean-variance Markowitz models. In the first work, we study naive strategies in the continuous-time mean-variance model. We propose a new type of agent to approximate the dynamic of the naive agent by partitioning the time line into numerous small equal length time intervals. Then, we prove that, the wealth process of the proposed agent converges to that of the naive agent and derive the explicit formula for the limiting wealth process and its corresponding portfolio process. In the end, we compare the naive strategies with two equilibrium strategies in the Black-Scholes market. The second work contributes to the mean-variance model by considering its distributionally robust counterpart, where the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by the Wasserstein distance. We reduce this problem to an empirical variance minimization problem with an additional regularization term. Moreover, we extend the recently developed inference methodology to our setting in order to select the size of the distributional uncertaint