Anomalous diffusion in trading models / Sidiq bin Mohamad Khidzir - Mohamad Khidzir, Sidiq (2010)
Econophysics is an interdisciplinary research field applying the mathematical methods of statistical physics to economics and finance. It emphasizes quantitative analysis of large amounts of economic and financial data as oppose to the more philosophical approach of political economics. A popular topic studied in econophysics is the distribution of wealth.Many models have been proposed to explain the trading dynamics [12,13] leading to the distribution of wealth universally observed in many countries. A more recent topic in econophysics is the movement of money studied by Brockmann in [19,20]. In this work, we are interested in studying the relation between the distribution of wealth and anomalous diffusion using a trading model. We plan to do this by studying the diffusion of money in correspondence to a particular trading model. In particular, our objective is to observe if the distribution of money displacement lengths and waiting times exhibit scale free behavior for a particular trading model. We conclude from the observations we made that a trading model with a resultant mixed distributions of wealth with a scale free tail exhibits anomalous diffusion. A trading model with a resultant mixed distributions of wealth with an exponential tail exhibits subdiffusion. A trading model with a resultant exponential distribution of wealth does not exhibit anomalous diffusion.