  We study a stochastic multiplicative system composed of finite asynchronous
elements to describe the wealth evolution in financial markets. We find that
the wealth fluctuations or returns of this system can be described by a walk
with correlated step sizes obeying truncated Levy-like distribution, and the
cross-correlation between relative updated wealths is the origin of the
nontrivial properties of returns, including the power law distribution with
exponent outside the stable Levy regime and the long-range persistence of
volatility correlations.
