The neoclassical price adjustment equation stipulates that prices move toward equilibrium at rate that is proportional to the excess demand, i.e., the difference between the demand and supply divided by the demand (at that price). However, the demand and supply are generally nonlinear functions...

The interaction between the volatility and price dynamics is explored. We model stochastic asset prices using the asset flow model with randomness arising directly from supply and demand. We show that the volatility is smallest at the extrema of the price. Linearizing the stochastic differential...

We consider a two-group asset flow model of a financial instrument with one group focused on price trend, the other on value. We prove the existence of both stable and unstable regions for the system of differential equations and show that a strong motivation based on (particularly recent) price...

A new set of methodologies extracts key nonlinearities in the dynamics of financial markets from data that would appear to be completely random with ordinary linear time series methods. The understanding acquired from this analysis forms a basis for modeling conflicting and competing motivations...

We derive a set of equations which are a simple model for investor behavior in a theoretical financial market. The model incorporates the emotional aspect of investor sentiment with memory of price history which decays exponentially in time. Within this model, the emotional reaction of the body...