Essays on Online Decisions, Model Uncertainty and Learning

Abstract

This dissertation examines optimal solutions in complex decision problems with one or more of the following components: online decisions, model uncertainty and learning. The first model studies the problem of online selection of a monotone subsequence and provides distributional properties of the optimal objective function. The second model studies the robust optimization approach to the decision problem of an auction bidder who has imperfect information about rivals' bids and wants to maximize her worst-case payoff. The third model analyzes the performance of a myopic Bayesian policy and one of its variants in the dynamic pricing problem of a monopolistic insurer who sells a business interruption insurance product over a planning horizon.