Positive Expected Feedback Trading Gain for all Essentially Linearly Representable Prices

We study a specific feedback stock trading rule, the simultaneously long short (SLS) strategy. This strategy is known to yield positive expected gains when the underlying stock returns are governed by a geometric Brownian motion or by Merton’s jump diffusion model. In this paper, we generalize these results to a set of price models called essentially linearly representable prices that are given by means of a set of stochastic differential equations based on (semi)martingales. Particularly, we show that the SLS trader’s expected gain is almost always positive and that it does not depend on the chosen price model but only on the trend. The basic novelties of this work are, first, the extension of the results in the literature to a set of SDEs and, second, that we do not need a solution of the SDEs, but we work on the level of SDEs directly, i.e., also for SDEs without or with unknown closed-form solutions positive SLS trading gains can be proven.