A dynamic herding model with interactions of trading volumes is introduced. At time $t$, an agent trades with a probability, which depends on the ratio of the total trading volume at time $t-1$ to its own trading volume at its last trade. The price r
eturn is determined by the volume imbalance and number of trades. The model successfully reproduces the power-law distributions of the trading volume, number of trades and price return, and their relations. Moreover, the generated time series are long-range correlated. We demonstrate that the results are rather robust, and do not depend on the particular form of the trading probability.
A simple trading model based on pair pattern strategy space with holding periods is proposed. Power-law behaviors are observed for the return variance $sigma^2$, the price impact $H$ and the predictability $K$ for both models with linear and square r
oot impact functions. The sum of the traders wealth displays a positive value for the model with square root price impact function, and a qualitative explanation is given based on the observation of the conditional excess demand $<A|u>$. An evolutionary trading model is further proposed, and the elimination mechanism effectively changes the behavior of the traders highly performed in the model without evolution. The trading model with other types of traders, e.g., traders with the MGs strategies and producers, are also carefully studied.
