Fat tail phenomena in a stochastic model of stock market : the long-range percolation approach

Using a Gibbs distribution developed in the theory of statistical physics and a long−range percolation theory, we present a new model of a stock price process for explaining the fat tail in the distribution of stock returns. We consider two types of traders, Group A and Group B : Group A traders analyze the past data on the stock market to determine their present trading positions. The way to determine their trading positions is not deterministic but obeys a Gibbs distribution with interactions between the past data and the present trading positions. On the other hand, Group B traders follow the advice reached through the long−range percolation system from the investment adviser. As the resulting stock price process, we derive a Lévy process.