Modeling a large population of traders: Mimesis and stability

We introduce a method of accurately and efficiently modeling a large population of participants in a financial market. Each participant is modeled as having an internal preference state affected by the continual arrival of exogenous information and by the behavior of others. In order to describe a community of traders, we introduce a population equation that is derived rigorously from the underlying single-agent model. The population equation is used to investigate collective behavior with mimetic interactions. We observe and study the sharp transitions in parameter space from a stable time-independent regime to instability where the demand and supply diverge sharply.