This research activity consists in the study of a new paradigm for automatic algorithmic trading started by Professor B. Ross Barmish that aims to treat stock trading from a control theory point of view. Within this approach robust performances are seeked against external disturbances and some levels of performances are guaranteed under certain assumptions. The main innovation introduced by Barmish is the developing of a new control scheme where stock price is treated as the external disturbance itself. This concept overturns the whole trading approach, stock price is no more the protagonist that one want to describe with some form of stochastic model and trying to predict with more accuracy that is possible, it becomes instead an uncertain external noise which effects one want to limit with the control system. The new control scheme is called Simultaneous-Long-Short (SLS) and the name derives from the fact that either long and short trade are performed in a simultaneous fashion, this guarantees non-negative gains under some assumptions on the price dynamics.
However, the classical SLS scheme has some problems and limitations and the aim of this project is to overcome them. The first limitation that has been identified in the classical scheme is that the controller was a simple time invariant gain. To overcome this limitation an adaptive algorithm, called Extremum Seeking was employed to vary adaptively the gain reacting to the variation of the prices. The second limitation that has been identified is the fact there is no consolidated strategy to tune the value of the controller to guarantee robustness of the performances. For this reason the original problem was reformulated in a Robust Control fashion where the controller were tuned using H_∞ synthesis to guarantee a certain level of robustness with respect to the range of variation of price returns giving birth to the Robust SLS scheme.