Posted by Pete Moss on July 15, 1997 at 19:23:43: In Reply to: Re: This is the million dollar question! posted by Bisser on July 15, 1997 at 17:00:45:They will not be equal, but log(E[1+b*R]) does not enter into the picture. We note only that expected bankroll growth is maximized when E[log(1+b*R)] is maximized. We can estimate E[log(1+b*R)] by plugging the first two moments of R, which we call the "ev" and the "v" respectively, into the first two terms of the Taylor's series expansion of log(1+b*R). We then set the derivative of that estimate with respect to b to 0, and solve for b, thus finding the b that maximizes the formula, and thus maximizes bankroll growth. I think this is really much simpler than you are imagining it to be.
Pete
- Re: E(log G) or E(G) Bisser 20:20:09 7/15/97 (3)