???

party pooper: May 3 2:40

Anonymous: May 2 4:35

Just to clarify my obtuse post, I was merely surprised that you simultaneously praise the authors, know about the Kelly criterion (to the extent you are teaching it), but not point out the redundancy of the paper that I pointed out. This isn’t an attack on you, especially if you were unaware of what I pointed out (hence my qualifier “if you know…”). In fact, if you didn’t know these details, that puts you in good company… of at least a few referees!

]]>Lones, you are right. If you know more than what you have written, you probably realized that most of this paper points out the well-known fact that if you bet more than “double-Kelly”, you eventually go bankrupt. This has been known for over half a century. (Anon’s post below is just one of many relevant citations.) In fact Theorems 1 and 2 are exactly variations on that fact. Half of Proposition 1 is also well known (e.g. that Kelly is myopic and unit-free). Finally: you can be bolder than log utility, have CRRA, and still get infinite wealth with probability 1. Exercise left to the reader.

]]>of the Fourth Berkeley Symposium on Mathematical Statistics and

Probability, ed. by J. Neyman, vol. 1, pp. 65–78, Berkeley. University of California

Press. ]]>

http://en.wikipedia.org/wiki/Kelly_criterion

and was used by Thorpe, the author of “Beat the Dealer” and “Beat the Market”, who also inspired the MIT Blackjack team, and ultimately that fun movie “21”. Paul Samuelson in 1969 tried to shoot it down as a smart investment strategy, seemed to think Thorp missed the bigger picture. It is clear that if one is living at all for the here and now, this is far too aggressive. Loosely, one might view this criterion as the optimal solution for delta=1. I have been pondering for some years the insights this has for optimal experimentation. I teach it every year in advanced theory hoping a crystalizing insight will strike me.

Meanwhile, those who want good fireside reading on this might peruse “Fortune’s Formula: The Untold Story of the Scientific Betting System that Beat the Casinos and Wall Street.”

]]>