On a New Paradigm for Stock Trading Via a Model-Free Feedback Controller

This paper describes a new paradigm for stock trading involving the use of classical feedback controllers which are “model free” in that they use neither parameterization nor estimation of stock price dynamics. At time t, the control signal is the investment level I(t), obtained via a mapping on the socalled gain-loss function g(t). While such strategies fall under the umbrella of technical analysis, our approach differs from the literature in a fundamental way: Whereas existing work in finance involves statistical analysis via historical back-testing, our new control-theoretic paradigm aims to provide “certification theorems” giving conditions under which certain robustness properties are guaranteed with respect to benchmark classes for the time-varying stock price p(t).We demonstrate our ideas using a linear feedback implementation of a new stock-trading scheme called Simultaneous Long-Short. The analysis is carried out in a so-called idealized frictionless market first using smooth prices for pedagogical purposes and then using a more realistic benchmark involving Geometric Brownian Motion. Finally, simulations are given which include real-world implementation issues.