Stock Trading via Feedback Control

1 Introduction

Stock trading involves the purchase and sale of shares of ownership in public companies by an individual or entity such as a pension fund, mutual fund, hedge fund, or endowment. These shares are typically traded in markets, such as the New York Stock Exchange and the NASDAQ, with the trader’s goal generally being to increase wealth. The words feedback control in the title of this article broadly refer to the use of information such as prices, profits and losses which becomes available to the trader over time and is used to make purchase and sales decisions according to some set of rules. That is, the size of the stock position being held varies with time. The mapping from information to the investment level is called the feedback law and is typically described with a closed-loop configuration and classical algorithms which come from the body of research called control theory; e.g., see Astrom and Murray (2008).

For simplicity, in this article, we restrict attention to...