ABSTRACT
This chapter gives an overview of stochastic optimization problems associated with market making. It describes the optimization model of Ho and Stoll and the recent advances by Avellaneda and Stoikov. The chapter includes an inventory constraint and subsequent extensions. It considers market making with both limit and market orders. The chapter gives an overview of smart order routing in fragmented primary markets and dark pools. It also considers the problem of optimal order splitting among exchanges and dark pools. The chapter discusses institutions and mechanisms of algorithmic trading, market microstructure, high-frequency data and stylized facts, time and event aggregation, order book dynamics, trading strategies and algorithms, transaction costs, market impact and execution strategies, risk analysis, and management. It covers market impact models, network models, multi-asset trading, machine learning techniques, and nonlinear filtering.
