On the use of model-free linear feedback to trade stock: Two open research problems

This paper is part of a new line of research involving the use of a model-free controller to trade stock. Motivated by robustness considerations, neither modelling nor identification of the stock price dynamics is involved. Instead, a time-varying investment level is generated using a “hardwired” feedback controller which processes states such as the cumulative gains and losses and the stock price. Within this framework, the focus of this paper is rather narrow: Beginning with existing results for the case of linear feedback, we provide a sampling of the type of research conducted in this evolving area by describing two open stock trading problems. We also include appropriate motivation for these problems and some background on stock trading so that the exposition can be followed by the uninitiated reader. As seen in the sequel, in addition to the development of theory characterizing performance of a trading strategy, an integral part of this research effort involves back-testing using historical stock market data.