Before revision:  This model is solvable using the theory of branching processes and the mean-field approximation  and displays a power-law cascade-size distribution-similar to the empirically observed one-over a wide range of parameters .
After revision:  This model is solvable using the theory of branching processes and the mean-field approximation and displays a power-law cascade-size distribution-similar to the empirically observed one. We further generalize the model to reproduce volatility clustering and other observed properties of real stocks .