Re: This is the million dollar question!

Posted by Bisser on July 15, 1997 at 17:00:45: In Reply to: Re: This is the million dollar question! posted by Pete Moss on July 15, 1997 at 13:32:04:


You are right. I was taking the limit outside the expectation, but E(lim B(N)/B(0)/N) is not equal to lim E(B(N)/B(0)/N) unless we bound B(N)/N by a constant. By the way, deriving the Kelly rule has the same problem.

Still, the log is arbitrary. As I noted in my other post, you are maximizing E(log lim B(N)/B(0)/N), and not log E(lim B(N)/B(0)/N). You cannot interchange the expectaion and the log.

Jensen's inequality says E(log(X)) =< log(E(X)). Do you have any reason to claim equality?

Bisser

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