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Evolutionary Model of Stock Markets

Joachim Kaldasch

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Abstract: The paper presents an evolutionary economic model for the price evolution of stocks. Treating a stock market as a self-organized system governed by a fast purchase process and slow variations of demand and supply the model suggests that the short term price distribution has the form a logistic (Laplace) distribution. The long term return can be described by Laplace-Gaussian mixture distributions. The long term mean price evolution is governed by a Walrus equation, which can be transformed into a replicator equation. This allows quantifying the evolutionary price competition between stocks. The theory suggests that stock prices scaled by the price over all stocks can be used to investigate long-term trends in a Fisher-Pry plot. The price competition that follows from the model is illustrated by examining the empirical long-term price trends of two stocks.

Date: 2015-05
New Economics Papers: this item is included in nep-evo, nep-ger and nep-hme
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Published in Physica A: Statistical Mechanics and its Applications, 415 (2014) 449-462

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