Algorithmic learning from financial predictions

We study how financial predictions can be used in learning algorithms for problems such as portfolio selection and derivatives pricing, from the perspective of minimizing regret; the worst-case loss (across all possible price paths) against some optimal benchmark model with superior information. Unlike most studies in financial mathematics, we do not make any underlying assumptions beyond the existence of such predictions, so our results are robust in the model-free sense. This thesis consists of three main ideas: 1. Study a portfolio selection model that competes with an optimal static trading strategy (the best fixed strategy in hindsight) using predictions of the optimal portfolio allocation. 2. Study a portfolio selection model that competes (in probability) with an optimal dynamic trading strategy (the best greedy strategy in hindsight) using price predictions of each asset in the portfolio. 3. Derive robust derivative pricing bounds for vanilla options and various exotic derivatives based on price predictions of the underlying asset(s). This work is focused on the mathematical analysis of these models, using techniques from theoretical algorithmic and statistical learning.