Convex Optimization, Stochastic Approximation, and Optimal Contract Management in Real-time Bidding

Abstract

This thesis studies problems at the intersection of monotone and convex optimization, auction theory, and electronic commerce. Convex optimization and the theory of stochastic approximation serve as the basic practical and theoretical tools we have drawn upon. We solve important problems facing Demand Side Platforms (DSPs) and other demand aggregators (to be defined in the main body) in the e-commerce space, particularly in the field of real-time bidding (RTB). RTB is a real-time auction market, the primary application of which is the selling advertising space. Our main contribution to this field, at its most basic, is to recognize that certain optimal bidding problems can be re-cast as convex optimization problems. Particular focus will be placed upon the second price auction mechanism due to the strikingly simple structural results that hold in this case; but many results generalize to the first price auction mechanism under additional assumptions. We will also touch upon formal connections between these auction problems and two important problems in finance, namely the dark pool problem, and optimal portfolio construction.