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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 return 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.
We study the daily trading volume volatility of 17,197 stocks in the U.S. stock markets during the period 1989--2008 and analyze the time return intervals $tau$ between volume volatilities above a given threshold q. For different thresholds q, the pr
The model describing market dynamics after a large financial crash is considered in terms of the stochastic differential equation of Ito. Physically, the model presents an overdamped Brownian particle moving in the nonstationary one-dimensional poten
This paper has been withdrawn by the authors.
Prospect theory is widely viewed as the best available descriptive model of how people evaluate risk in experimental settings. According to prospect theory, people are risk-averse with respect to gains and risk-seeking with respect to losses, a pheno
Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of distributions