I think some of you know the famous billionaire mathematician James Simons. Somewhat as Warren Buffet, this guy cracked the Wall Street with a mathematical model (essentially most statistic and a bit of probability). It could take a lot of time, but I'd like to understand by myself how he constructs his model or how to reproduce a similar model. It follows that none idea came up so far, and I wish someone would unblock me at this level.
Questions : Could anyone be able to give me a path, ideas (Markov models, ...) how could I obtain a starting idea? In other words, does anyone have the intuition of the mathematical theory he uses to this algorithm?
Few things have been stated in public.
One is that the first modeler at Renaissance was co-inventor of the Baum-Welch algorithm for estimating Hidden Markov models, so one would assume that some sort of Markov or HMM models were tried at an early stage.
Another is obtaining data. Simons purchased the historical data on limit order books at the exchanges, in the 1970's. I don't know at what point his competitors did the same, but it is possible that Renaissance had a head start in data analysis.
A third is the use of Kelly betting. This was also known to, and used by, Ed Thorp and his fund.
There was also a lawsuit in the past 10 years, by Renaissance against a former employee, that disclosed some vague and limited information in the court papers, but I don't think you will find there any mention of specific methods or algorithms.