A price dynamic equilibrium model with trading volume weights based on a price-volume probability wave differential equation

Guided by a price-volume probability wave differential equation in a new mathematical method, we study intraday market dynamic equilibrium in stock market. We select intraday cumulative trading volume distribution over a price range as individual mental representation and determine a price equilibrium point by the maximum volume utility price. We propose the hypothesis that a stock price can deviate away from the equilibrium point in momentum and restore to it in reversal, and the volume distribution embodies market dynamic equilibrium. Then, we examine it by a set of explicit price dynamic equilibrium models with trading volume weights from the differential equation against a large number of the price-volume distribution using tick-by-tick high frequency data in Chinese stock market in 2019. It holds true. We can infer that the theory is applied for a broader scope because it embraces core mathematical components in expected utility theory, prospect theory, and reflexivity theory. •To select intraday cumulative trading volume distribution over a price range as individual revealed preferences;•To determine a price equilibrium point in beliefs by the maximum trading volume utility price;•To interpret individual trading utility function in stock market;•To study intraday nonlinear market dynamic equilibrium where price behaves momentum and reversal;•To examine it by a set of explicit models in a new mathematical method.