Field in mathematics for forecasting price of stock markets

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Hi i'm just learned somethings about technical analysis and some stuff about indicators?

Here is my questions:

Does Technical analysis based on Mathematics so we can trust it?

Which filed of mathematics help us for doing analysis and forecasting price movment in financal markets ?

Can we really predict price movment with mathematics or other sciences?

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This is not my area of expertise, but my understanding is that one uses Ito calculus to write down "differential equations" of random variables. We model markets based on such differential equations. My understanding is that a broader class of models known as Levy processes can also be used.

A famous model in this domain is known as the Black-Scholes equation which governs price evolution in certain types of options.

In general, looking at quantitative finance / mathematical finance is the keyword you are looking for.

Since I believe you are a programmer, this collection of IPython notebooks that build up the theory of quantitative finance is invaluable.

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In addition to what has been posted, this paper gives a nice overview of the areas of mathematical finance, and what type of mathematics are involved in each.

As far as technical analysis goes, I've only seen momentum indicators referenced as viable strategies in some cases within academia. Though, no one would be quick to publish results if they found otherwise.