2013/10/31 by V. M. Zharkov, Zharkov, Viktor
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Economics and business #FOS: Physical sciences #Opinion Dynamics and Social Influence #Strongly Correlated Electrons (cond-mat.str-el) #Trading and Market Microstructure (q-fin.TR) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1310.8431
openalex publication_date 2013/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new multiagent model of the stock market is formulated that contains four states in which the agents may be located. Next, the model is reformulated in the language of the functional integral containing fluctuations of prices and quantities of cash flows. It is shown that in the functional integral of that type description of the prices is given not by the real numbers as is made in many papers but the p-adic numbers. It is shown in the following simple examples extracted from the proposed theory that the p-adic description of prices gives good description of fractal behavior of the trends. The formula is given for the p-adic mapping of prices. Using this formula we obtain the main p-adic patterns which are the same as the patterns of Elliott wave theory, this fact allows us to give a rigorous mathematical proof of this theory. Our model is the only model that gives a strict point like description of the fractal behavior of prices. The developed approach opens the possibility to give the formulation of p-adic technical analysis of the stock market.