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 so-called 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. [ABSTRACT FROM AUTHOR]