  Far-from-equilibrium models of interacting particles in one dimension are
used as a basis for modelling the stock-market fluctuations. Particle types and
their positions are interpreted as buy and sell orders placed on a price axis
in the order book. We revisit some modifications of well-known models, starting
with the Bak-Paczuski-Shubik model. We look at the four decades old Stigler
model and investigate its variants. One of them is the simplified version of
the Genoa artificial market. The list of studied models is completed by the
models of Maslov and Daniels et al. Generically, in all cases we compare the
return distribution, absolute return autocorrelation and the value of the Hurst
exponent. It turns out that none of the models reproduces satisfactorily all
the empirical data, but the most promising candidates for further development
are the Genoa artificial market and the Maslov model with moderate order
evaporation.
