Approaches of both theoretical analysis and computer simulation are used to study a stochastic multi-agent stock market model. Theoretical analysis provides the parameter settings for different dynamic regimes including fundamental equilibrium, non-fundamental equilibrium, periodicity and chaos. Agent-based computer simulations with those settings are performed to produce the price series. Statistical analysis of these data shows: markets of all regimes present stylized facts such as fat-tail, volatility clustering and long-term memory; the fundamental equilibrium regime has the most significant stylized facts, followed by periodicity and chaos, and non-fundamental equilibrium the least.