CDC semi-plenary: “On stock market modeling and trading: New problems for the control field”

The objective of this semi-plenary is to describe a new model for stock and option trading based on control theoretic considerations. The controller is taken to be the amount invested over time and we consider various measures of performance such as trading profit, draw-down and value at risk. In contrast to classical approaches to trading which are based on a stochastic Wiener process description for the evolution of the stock price, our new paradigm involves a rather standard low order state space model and control is implemented via a classical static output feedback. In addition to simplicity of this new formulation, another factor motivating this new line of research is the following: Approaches to trading in the literature, based on the use of a Wiener process for stock price prediction, typically involve the questionable assumption that historical volatility can be used “going forward.” Said another way, in the case of most past literature, price volatility is assumed to be time-invariant. In recognition of the time-varying “character” of volatility, our new approach does not include a stochastic model for the evolution of stock price. Instead, we simply treat the stock price as an external uncontrolled input belonging to a rather unstructured family P. Given the setting above, we seek to provide various robust performance certifications with respect to the family P. For example, an important goal is to robustly guarantee “excess returns” which exceed some standard benchmark such as buy-and-hold. Finally, the obvious should be noted: Robust performance guarantees involving the model do not imply that the same performance will result when a real time series for stock price is substituted for the price. Therefore, an integral part of this line of research involves extensive back-testing using data derived from real financial markets.