Re: Reasons for Kelly

Posted by Bisser on July 14, 1997 at 20:06:48: In Reply to: Re: Reasons for Kelly posted by Pete Moss on July 14, 1997 at 17:10:05:


Thanks, now I feel that I am getting closer :)

Let G = lim{B(N)/B(0)/N} as N --> infinity. From what you wrote I see that you maximize E(log(G)) and not E(G) (the log and the expectation cannot be interchanged, unless G is a constant). Maximizing E(G) will give you the "greedy" advice: bet the farm (your total bankroll) when R has positive expectation.

So when you wrote "To maximize this product, it is sufficient to maximize its logarithm", it seems things went a little sour (or I am missing something in the argument).

If we try to maximize the limit of log(B(N))/log(B(0))/N then everything you wrote works fine. In this is the case we should clearly state that we use "utility = log(money)". After all, "utility = log(money)" is not such a bet approximation to the value of money...

Bisser


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