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# PhD-Project "Feedback-based trading strategies on noisy markets"

Project Leader: Prof. Dr. Lars Grüne
Prof. Dr. Bernhard Herz
Contact: Prof. Dr. Lars Grüne

start of the project: 2014/03/01, end of the project: 2015/10/14

Project team:

Support:

Michael H. Baumann is supported by a scholarship of Hanns Seidel Stiftung e.V. (HSS), by means of Bundesministerium für Bildung und Forschung (BMBF).

## BACKGROUND

When trading assets listed at the stock exchange, e.g., company shares, the question for choosing an appropriate trading strategy arises. Apart from so called fundamentalist strategies, which compare the stock price with the fundamental value of the firm, there are also technical strategies, in which the decision about buying and selling is exclusively taken based on information derived from the price chart. Traders following such strategies are consequently called chartists. While many economists consider these strategies as no better than reading tea leaves, they are nevertheless quite popular in practice. Since a couple of years control theorists have tried to rigorously establish performance properties of such strategies - with some surprising results.

## CONTRIBUTION TO THE MISSION OF MODUS

In the PhD project "Feedback based trading strategies on noisy markets" trading strategies for asset portfolios are formally modelled using methods from mathematical control theory. On the one hand, characteristics of the resulting strategy like its expected gain and its variance are analyzed in a mathematically rigorous way. Here the so called price taker property is assumed, i.e., that the trading strategy has no impact on the stock prices, which are modelled by stochastic differential equations. On the other hand, the economic impact of using such strategies and its interplay with other trading strategies is studied. To this end, the formation of prices on the stock market is modelled phenomenologically by a market maker model. Using both simulations and analytical methods one can then analyze effects like changes in volatility or the probability of bubbles in the market.

## RESULTS

For a certain feedback based trading strategy, the so called Simultaneously-Long-Short-Strategy (SLS), it was known before that a positive gain can be expected if stock prices are described by the (almost surely continuous) paths of a geometric Brownian motion. In the project it could be shown that this property remains true if prices are governed by Merton's jump diffusion model, whose paths are almost surely discontinuous. This result could be further extended to an even more general price model. Furthermore, a market maker model was developed for investigating the interplay between feedback traders, noise traders (i.e., traders which act randomly) and fundamentalist traders. In this setting it could be shown that fundamentalists, which are expected to stabilize the market, may not have this ability when acting on a market together with feedback traders, even when the fundamentalists are equipped with unlimited ressources. Current research deals with extending these results to markets with multiple assets and further analyzing the limitations of the stabilizing effects of fundamentalist traders.

responsible for the content: Lars Grüne