Modern Algebra, Calculus, Topology, Number Theory, Theory of Computation. I can follow most graduate texts in any of these fields. I am very weak in Calculus, very strong in Algebra and Number Theory. No degree. nitro
Here's a link: http://socrates.berkeley.edu/~hdreyfus/html/paper_socrates.html I'm just trying to help the 17th century Mathematicians... Personally for me, I still have problems understanding Galileo, Kepler and etc.. I just recently realized that the Earth was round and we orbit around the Sun.... But I still develop systems.
hmm. i doubt any smart physicist would apply it to the markets. i had one very smart math wiz kid within my team for half a year and discussed this kind of thing at length with him. and he was quite sure that the kind of challenge the market shows is simply easier and more efficient tackled with other tools than highest math. now that clearly does not mean a thing, since he was ... a kid ... . my current understanding is that there are different ways to describe the market. more complex and more simple ones. i for myself would love more complexity only for one reason: higher entrance barriers, means edge lasting longer. now i am setting up a project were i let different people describe the market with their tools, be it fractals or nn or whatever. and honestly speaking i know by far to little to imagine that superstring theory does well in timeseries analysis - so it is not on my list. not to speak of the difficulty to find someone really within the subject ... then i gonna take their description, spells: a number of additional time series and try to find whether they or combinations of them have prediction power above randomness. sounds very simple but took me literally years to get to it. see, my problem was that my backtesting people are handson practioners who do not at all want to dig into agent based models for three months before they have their first backtest running. and the theoretically profound people struggle with backtesting in the first place or with the assumptions and ifs and whens of testing or with the fact that all the effects are very small on their own. but letting the theorist only describe while leaving the interpretation to the practioner i (hope to) overcome this problem. btw what do you think about john hagelin?
Thunderdog, there are some decent models based on marked point processes that explain a surprising amount of real-life trading processes. You are right though, in that most models come nowhere close to modelling real life. Complexity theory is really interesting stuff though, agent based models, complex simulations, etc are all getting closer but I suspect all the accurate models are highly proprietary. http://www.time.com/time/magazine/article/0,9171,1187290,00.html
surf, hmm. i doubt any smart physicist would apply pure string theory to the markets. i had one very smart math wiz kid within my team for half a year and discussed this kind of thing at length with him. and he was quite sure that the kind of challenge the market shows is simply easier and more efficient tackled with other tools than highest math. now that clearly does not mean a thing, since he was ... a kid ... . my current understanding is that there are different ways to describe the market. more complex and more simple ones. i for myself would love more complexity only for one reason: higher entrance barriers, means edge lasting longer. now i am setting up a project were i let different people describe the market with their tools, be it fractals or nn or whatever. (and honestly speaking i know by far too little about it to imagine that superstring theory does well in timeseries analysis - so it is not on my list. not to speak of the difficulty to find someone really within the subject ...) then i gonna take their description, spells: a number of additional time series and try to find whether they or combinations of them have prediction power above randomness. sounds very simple but took me literally years to get to it. see, my problem was that my backtesting people are handson practioners who do not at all want to dig into agent based models for three months before they have their first backtest running. and the theoretically profound people struggle with backtesting in the first place or with the assumptions and ifs and whens of testing or with the fact that all the effects are very small on their own. but letting the theorist only describe while leaving the interpretation to the practioner i (hope to) overcome this problem. btw what do you think about john hagelin?
Thunderdog, Not wanting to let you wait too long, I would answer with a 17th century story. Blaise Pascal, was a genius in many fields. He was an invalid from childhood. He constructed the first (or second?) mechanical calculator, he had a tremendous influence in shaping the modern French language as a writer. He published many religious works. As a mathematician his theory on conical sections is practically still taught today the way he wrote it, he discovered the fact that gases have mass (weight), he was active in number theory and last but not least, he is credited with the invention of probability theory. What motivated Blaise Pascal was finding answers to kind of the identical problem you raise. He (and his correspondent Fermat) tackled the problem posed by "The Games of Chance". No known mathematical approach was appropriate for dealing with this problem - not unlike the coclusion you arrived at. Not going into the intricacies of 17th century mathematical reasoning, let's stick to a simplified modern description. What happens is that original variables connected to causes in a most complicated way, causes sometimes not or only partially understood, are replaced "wholesale" by one or more probabilistic variables. These variables are made to obey rules which can be verified as being representative for the original problem. This is model-building. Applying input variables to such probabilistic model will yield outputs useful in predicting the outcome of the real process. All this holds of course insofar the probabilistic model is truly representative for the problem at hand. Over the years, an impressive corpus of mathematical knowledge has risen: Probability Theory, Statistics, Stochastic Processes. True mastery of these fields is unthinkable without a thorough schooling in the underlying theories. I did my best to stay within the framework of your question and thought that referring to the historical background was rather revealing. Undoubtedly, some will do better. nono
I think two points are important here. 1) the point is not to predict the future, but rather to know the past. You don't have to predict the human behavior, but to understand how the human behavior has been, and how it reacts to specific circumstances. 2) the human behavior of one person is not always consistent, but the behavior of thousands (or millions) of people mostly is. If a huge amount of people have proven to behave in a specfic way when some specific events occur, maybe when those events occur again not all of these people will do the same, but a vast majority will. Of course, you have to find out what the causes of some specific behavior are. This is mostly very difficult, and never accurate at 100% If you consider this, I think yes, you can predict human behavior, to a fair degree of precision.
Here we go again. The purpose of the exercise is to indeed PREDICT the FUTURE. At the origin of probability theory, when Pascal & Fermat were looking at "Games of Chance", what would have been their motivation other than to predict the outcome of the game, given of course the relevant data available at the start and during this process. Nobody, except for some ET diehards, ever insisted that prediction in the probabilistic sense MUST have a 100% accuracy. That's why we have probability theory in the first place. Now, don't misunderstand me. All this does not lead to a quick and easy recipe for beating the markets. Markets these days are shaped by many very savvy strategists fully conversant with such techniques. If you want to win, don't forget that you play against the most clever people money can buy: you got to be as smart or better a little bit smarter. That's also why nobody is going to give away any nitty gritty. Only quacks will pretend to do so (against payment of course). nononsense