Since Bachelier  in 1900 , when mathematical finance began, attempts at understanding the nature of stock market prices and at predicting them have not succeeded. Statistical models have only found minor regularities and anomalies. Other approaches have failed or are illusory. To this day, the physicists and mathematicians working in economy consider that the evolution of security prices is basically random, and, thus,  not predictable. We show that the evolution of security prices not at all random but is largely deterministic and , more remarkably, governed by a physical law. The law takes the form of a physicomathematical theory centered around a purely mathematical function (not a model and unrelated to statistical methods). The function can be described as an "isodense" network of "moving " regression curves of an order greater than or equal to 1. When inputting a time series of any security into the function, new mathematical objects emerge spontaneously  . The graphical representation of the function is called a "topological network"  and the emergent objects are called "characteristic figures" (mainly "cords"). What is central to the function is that these cords have the unique property of attracting and repelling the price , so that the price bounces from one cord to another. The direct consequence is that prices are driven by the cords in a semi-deterministic manner (leaning towards deterministic). Having a function that describes the evolution of the price, we now understand the reason behind each price movement and can predict stock prices both qualitatively and quantitatively. The function is universal, does not rely on any fitting, and, thanks to its extreme sensitivity, reveals the hidden order present in time series data that other methods have never uncovered.
Since Bachelier 's thesis in 1900 (laying the foundation of the stochastic process, or Brownian motion, as a model of stock price changes), attempts at understanding the nature of prices and at predicting them have failed. Statistical methods have only found minor regularities /anomalies, and other mathematical and physical approaches do not work. This leads researchers to consider that the evolution of security prices is basically random, and, thus, inherently not predictable. We show that the evolution of security prices is not a stochastic process but largely deterministic and governed by a physical law. The law takes the form of a physicomathematical theory centered around a purely mathematical function , unrelated to models and statistical methods. It can be described as an "isodense" network of moving regression curves of an order greater than or equal to 1. The salient aspect of the function is that, when inputting a time series of any security into the function, new mathematical objects emerge spontaneously , and these objects exhibit the unique property of attracting and repelling the quantity . The graphical representation of the function is called a "topological network" due to the preeminence of shapes over metrics, and the emergent objects are called "characteristic figures" (mainly "cords"). The attraction and repulsion of the price by the cords results in the price bouncing from cord to cord. Thus, the price has to be considered as driven by the cords in a semi-deterministic manner (leaning towards deterministic). With a function that describes the evolution of the price, we now understand the reason behind each price movement and can also predict prices both qualitatively and quantitatively. The function is universal, does not rely on any fitting, and, due to its extreme sensitivity, reveals the hidden order in financial time series data that existing research never uncovered.
A
's thesis
R
, when mathematical finance began,
(laying the foundation of the stochastic process, or Brownian motion, as a model of stock price changes),
D
stock market
R
not succeeded. Statistical models
failed. Statistical methods
R
and anomalies. Other approaches have failed or are illusory. To this day, the physicists and mathematicians working in economy
/anomalies, and other mathematical and physical approaches do not work. This leads researchers to
A
inherently
R
not at all random but is
is not a stochastic process but
D
, more remarkably,
R
(not a model and unrelated to statistical methods). The function
, unrelated to models and statistical methods. It
R
"moving "
moving
R
When
The salient aspect of the function is that, when
A
, and these objects exhibit the unique property of attracting and repelling the quantity
A
due to the preeminence of shapes over metrics,
R
What is central to the function is that these cords have the unique property of attracting and repelling the price , so that the price bounces from one cord to another. The direct consequence is that prices are
The attraction and repulsion of the price by the cords results in the price bouncing from cord to cord. Thus, the price has to be considered as
R
Having
With
R
predict stock
also predict
R
thanks
due
R
present in
in financial
R
other methods have
existing research