Effects of linear feedback trading in an interactive market model

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.