Dresden 2006 – scientific programme

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AKSOE: Physik sozio-ökonomischer Systeme

AKSOE 12: Economic Models and Evolutionary Game Theory II

AKSOE 12.2: Talk

Thursday, March 30, 2006, 10:45–11:15, BAR 205

Stock markets as adaptive controllers — •Klaus Pawelzik and Roland Rothenstein — Inst. f. Theor. Physik, Otto-Hahn Allee, D-28334 Bremen

Price time series from large speculative markets exhibit power law distributions of returns and temporal correlations of fluctuation amplitudes (volatility clusters). These ’stylized facts’ appear to reflect ’irrationalities’ of the market’s participants which challenges the hypothesis that the price dynamics cannot be exploited for making arbitrage profits. We reformulate this ’efficient market hypothesis’ as successful control. Our investigations of a simple market model with nonadaptive agents indeed demonstrate that already the redistribution of goods by trade via an order book suffices to realize adaptation of the overall system which rapidly compensates the effect of predictable external drives on the price. The residual fluctuations, however, are found to remain non-gaussian if the market is dominated by speculative agents. To understand the origin of these power law fluctuations we analyse the dynamics of an optimal adaptive controller with very short memory when applied to an unstable one-dimensional system. We find that this system is attracted to a state in which the external noise is critically amplified. Analysis demonstrates that this ’self-organized critical control’ generally causes power law fluctuations of the residuals. Our results suggest that the large fluctuations of returns observed in real markets rather are the neccessary consequence of successful control than reflecting inefficiencies.