ABSTRACT
A Market Maker (MM) is an individual or an agent, who actively provides bids and offers asks in a financial market. Her main goal is to maximize her profit and loss functional by getting the bid-ask spread. The purpose of this chapter is to provide a literature review to explain dynamics of the market making, the impacts of the market orders on the limit order book, adverse selection and inventory risks exposed by an MM. We present several results of the algorithmic and high frequency trading via stochastic optimal control; especially by Dynamic Programming Principle. Furthermore, the optimal spreads and the corresponding value functions are described based on the trade of the risky assets and the options. On the other side, market making is a type of High Frequency Trading. Consequently, all technological and regulatory conditions are strongly related to MMs. In this context, the necessity of the new investigations for algorithm developments are shining, such as Reinforcement Learning (RL) techniques. Hence, this chapter is finalized by giving an insight and an outlook for future works from both theoretical and numerical aspects.
