On the basics for simulation of feedback-based stock trading strategies: An invited tutorial session

This paper provides an overview of our CDC tutorial session covering the basics of simulation and performance evaluation associated with stock trading via feedback control methods. The specific trading algorithms which we describe fall under the umbrella of “pure technical analysis” in that they are model-free with no parametrization of the stock-price process assumed. True to technical analysis, we adopt the point of view that the stock price p(t) is an external input with no predictive model for its evolution. The feedback controller adapts the investment level I(t) based on the evolution of the trading gains or losses over time. In the introductory talk, it is explained how this point of view “opens doors” for new research contributions from the control community. The simulations which we consider are of two types: In some cases, the controller's performance is studied using synthetic classes of stock prices such as Geometric Brownian Motion. In other cases, real historical prices are brought into play. We refer to such a real-price simulation as a “backtest.” Once we cover the trading mechanics, the notion of “benchmark price classes,” data acquisition and coding of algorithms, the focal point becomes performance evaluation. That is, with g(t) denoting cumulative gains or losses, we describe a number of metrics which are used to evaluate the performance associated with the trajectory pair (I(·), g(·)). Whereas the first half of the tutorial concentrates on trading a single stock, the last half addresses multi-asset portfolios, educational aspects and the notion of trading competitions.