Abstract-In the literature a lot of articles about so-called feedback-based trading strategies, i.e., strategies that compute investment exclusively from their own gain exist. Price is therein treated as a disturbance variable in the technical application. With these strategies, astonishing results may be shown. However, the so-called price taker property is always assumed, that means that one's own trading does not affect the price, which is quite unrealistic. In the work at hand, an interactive and thus more realistic market model is introduced which is completely determined by the traders' decisions. In this market model, distinct groups of traders can interact, e.g., feedback traders and noise traders, as they are considered to be relevant in economics in explaining real market prices. Furthermore, this interactive market model is a natural generalization of the geometric Brownian motion. Of course the model has to be bubble-prone to be realistic. The market model will be analyzed as well as the effects of linear feedback strategies and trading restrictions on the price. A way to calculate thresholds for the parameters to cause bubbles is provided. To conclude the work, backtesting on real market data is performed.
I. MOTIVATION AND INTRODUCTIONIn recent years, a lot of papers about the use of feedbackbased trading strategies on financial markets, e.g. [4] and [5], were published. Therein, control theoretical ideas, well known in the engeneering sciences, have been adapted to financial market models. Trading strategies, i.e., the amount of bought and sold shares at each point of time, are defined without any assumptions about the market model, like the geometric Brownian motion or other stochastic models, and no enterprise data or business information is considered, thus, pure feedback strategies are applied. These methods are covered by the term "technical analysis". With this, remarkable results may be shown like, for example, the existence of arbitrage opportunities, see [3]. For obtaining these results, among a few technical assumptions also the so-called price taker property is assumed, which means, that one's own trading does not influence the price. This is, of course, a justified supposition if small investors are regarded, but usually these small investors do not use feedback strategies, as this would exceed their capabilities. However, controlbased trading is used by large investors like funds, which violate the price-taker assumption.The work at hand provides a market model which does not only allow prices to be influenced by the traders but also that the price is determined by the traders' buying and selling decisions. The model will be discussed and different trading strategies will be established. All traders influence the price process and possibly, indirectly each other, too.The author is with Faculty of Mathematics, Physics and Computer Science, University of Bayreuth, 95447 Bayreuth, Germany michael.baumann@uni-bayreuth.de An important ingredient of our model are the so-called noise traders...