Distributions

Once upon a time I looked at the problem of finding the relationship between the Standard Deviation of stock returns and stock prices. Indeed, Bollinger Bands use the SD of prices (over the past umpteen day) to provide Buy & Sell signals. Anyway, the problem (mathematically speaking) might go like this: You have a set of returns, {X}, with a known distribution. You pick n at random and calculate: Z = (1+X1)(1+X2)...(1+Xn). Them's the prices, eh? So what's the distribution of the Zs? After thinking about it, off and on (for years), I figured I was just too schtoopid to solve the problem -- even if I assumed the set of returns were Normally distributed. (Math-types always make such simplifying assumptions.) Then I recently ran across some papers about the distribution of the product of just two random variables. It involves (are you ready?) K0. He's a Bessel function. I met him before. Then I run across a paper dealing with the distribution of the product of three random variables. It involves Meijer G-functions. Huh? I ain't never met her before. Somehow, I feel better ... and I'll give up this quest 'cause I now know I am too shtoopid