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An interesting argument, and a good intuition for why the Kelly criterion is good. As far as it relates to my comment and comment: I think you're advancing a t
by kevinwang 5y ago
An interesting argument, and a good intuition for why the Kelly criterion is good.
As far as it relates to my comment and comment: I think you're advancing a third answer to the "why" question, not showing why "maximizing expected geometric growth" is a better "why" than "maximizing (logarithmic) utility".
With that said, I still think the "maximizing (logarithmic) utility" answer is the only good motivation. My reasoning is that most people (myself included) define rationality to be: maximizing expected utility. From this, we can derive the Kelly criterion.
- rssoconnor 5y agoWhether it is a third "why" or not is a bit philosophical. I think the property I stated leans heavy towards arguing for maximizing expected geometric growth, because this property has nothing to do with the notion of utility. Indeed, no matter what you utility function is, as long as it is strictly monotone, it will be the case that a Kelly strategy always eventually permanently yields a bankroll with more utility than any other strategy. This holds for the simple reason that when reinvesting profits into the next bet, you must reinvest actual money, not utility. As for me, I often waffle between thinking this Kelly property I stated is important versus expected utility of some sort.