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I wander whether there is a theory that explains the stock exchange behavior (or a single stock) by assuming some transitions between (maybe almost) well defined states. If, I will appreciate a short explanation of the theory or a reference to it. Thanks!

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    It's not clear what you are asking for. My guess from the OP is you may be attempting to model the operations of a stock market or brokerage for an enterprise software design? – user662852 Jan 7 at 20:39
  • Can I ask your skills in math and statistics? Are you comfortable with calculus? Have you any coursework in probability or statistics? How much economics do you know? Would you be able to discuss marginal changes in some variables comfortably? Is this a curiosity question or do you have a practical plan in mind? – Dave Harris Oct 5 at 20:44
  • I am asking because how you answer will impact how I answer. Plus, mathematical notation is not available on this forum, so it requires a bit of an extended discussion if the best answer is math intense. – Dave Harris Oct 5 at 20:45
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Your question asks about the behavior of a stock exchange as a whole and the behavior of a single stock. You need to clarify what you're looking for.

There's the Efficient Market Hypothesis which is about the market as a whole. Personally I think it's garbage. Here it is in some detail: https://www.investopedia.com/terms/e/efficientmarkethypothesis.asp

There's Modern Portfolio Theory, which is the cornerstone of 95% of the investment industry. It breaks down a bit in times of extreme volatility and increased correlation between markets. More details here: https://www.investopedia.com/managing-wealth/modern-portfolio-theory-why-its-still-hip/

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