On theoretical foundations of mostly model-free cross-coupled simultaneously long-short stock trading controllers

Abstract

In the last decades, feedback trading and especially simultaneously long-short (SLS) trading attracted a lot of attention in the control community. The main reason for this is the so-called robust positive expectation property, which states that under specific conditions like, e.g., continuous time trading and survival the SLS controller achieves for almost all (a.a.) parameter settings, positive expected gains not only for several price models but also in mostly model-free frameworks. In finance, topics like optimal pairs trading are of interest for research and implementation. In the intersection of pairs trading and SLS so-called cross-coupled SLS (CC-SLS) rules are analyzed. Typically the CC-SLS rule is analyzed either empirically or with specific model assumptions. In the work at hand, under specific assumptions we do not only show that a new type of cross-coupled SLS (CC*-SLS) rule achieves the robust positive expectation property but also that this CC*-SLS is in expectation for a.a. parameter settings superior to the standard SLS rule used stock by stock. Furthermore, we perform simulations to illustrate the controllers’ behavior.