# A Price Dynamic Equilibrium Model with Trading Volume Weights Based on a Price-Volume Probability Wave Differential Equation

44 Pages Posted: 2 Dec 2019 Last revised: 26 Jul 2021

See all articles by Leilei Shi

## Leilei Shi

Haitong Securities Co. Ltd.----Beijing Fuwaidajie; Haitong Securities Co. Ltd.----Beijing Fuwaidajie; International Institute of Finance, School of Management, University of Science and Technology of China (USTC)

## Bing-Hong Wang

University of Science and Technology of China (USTC) - Department of Modern Physics

## Xinshuai Guo

University of Science and Technology of China (USTC) - School of Management

## Honggang Li

Beijing Normal University (BNU) - School of Systems Science

Date Written: August 15, 2020

### Abstract

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 for 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.

Keywords: Behavioral finance theory, Mathematical method, Market dynamic equilibrium, Volume distribution over price, Momentum and reversal

JEL Classification: G40, C61, D53, B41

Suggested Citation

Shi, Leilei and Shi, Leilei and Wang, Bing-Hong and Guo, Xinshuai and Li, Honggang, A Price Dynamic Equilibrium Model with Trading Volume Weights Based on a Price-Volume Probability Wave Differential Equation (August 15, 2020). International Review of Financial Analysis Volume 74, March 2021, 101603, Available at SSRN: https://ssrn.com/abstract=3496068 or http://dx.doi.org/10.2139/ssrn.3496068

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