A simple trading model based on pair pattern strategy space with holding periods is proposed. Power-law behavior is observed for the return variance σ2, the price impact H and the predictability K for both models, with linear and square root impact functions. The sum of the traders’ wealth displays a positive value for the model with a square root price impact function, and a qualitative explanation is given based on the observation of the conditional excess demand 〈A|u〉. The cumulative wealth distribution also obeys a power-law behavior with an exponent close to that of real markets. An evolutionary trading model is further proposed. The elimination mechanism effectively changes the behavior of traders, and a power-law behavior is observed in the measure of zero return distribution P(r=0). The trading model with other types of traders, e.g., traders with the MG’s strategies and producers, are also carefully studied.
