But, I was slightly disappointed by the framing of Kelly as a choice of SWF.
1. Kelly is inherently a repeated-bet framework. Because each stake is set as a fraction of current wealth, every round’s outcome mechanically alters the base for the next one. That path-dependence links the bets and makes log-utility the right objective. It is just targeting a growth-rate of your betting *policy* from 1-shot bets.
2. If the terminal horizon isn’t truly terminal, you’ve already assumed a growth-rate objective. Once you care about wealth in the next period (or the one after that), you’re back to maximizing geometric mean growth—that’s exactly what the Kelly fraction does. If instead the game genuinely ends at T, solve the one-shot expected-utility problem and leave Kelly out of it.
Thanks for the deep and insightful comment. You’re 100% correct that Kelly is a repeated bet framework, and not obviously directly applicable to end of the world scenarios.
Heres the sense in which i brought it up:
1) i know utility = log(wealth) is one way of generating Kelly betting as the optimal decision — im pretty sure this is the case even in the 1-shot setting
2) in the papers we read, the authors consider log(consumption) as a utility function, and say it allows for a remarkable amount of risk
So i didnt mean to imply that Kelly was directly applicable to a setting with an end — rather im trying to give context for how risky log utility “feels” in non existential settings.
Thought I'd let y'all know: on Apple Podcasts atm, your episodes can't be played and your podcast can't be followed. "Podcast cannot be added because the server or feed cannot be found."
Big fan of the show
But, I was slightly disappointed by the framing of Kelly as a choice of SWF.
1. Kelly is inherently a repeated-bet framework. Because each stake is set as a fraction of current wealth, every round’s outcome mechanically alters the base for the next one. That path-dependence links the bets and makes log-utility the right objective. It is just targeting a growth-rate of your betting *policy* from 1-shot bets.
2. If the terminal horizon isn’t truly terminal, you’ve already assumed a growth-rate objective. Once you care about wealth in the next period (or the one after that), you’re back to maximizing geometric mean growth—that’s exactly what the Kelly fraction does. If instead the game genuinely ends at T, solve the one-shot expected-utility problem and leave Kelly out of it.
Thanks for the deep and insightful comment. You’re 100% correct that Kelly is a repeated bet framework, and not obviously directly applicable to end of the world scenarios.
Heres the sense in which i brought it up:
1) i know utility = log(wealth) is one way of generating Kelly betting as the optimal decision — im pretty sure this is the case even in the 1-shot setting
2) in the papers we read, the authors consider log(consumption) as a utility function, and say it allows for a remarkable amount of risk
So i didnt mean to imply that Kelly was directly applicable to a setting with an end — rather im trying to give context for how risky log utility “feels” in non existential settings.
Thought I'd let y'all know: on Apple Podcasts atm, your episodes can't be played and your podcast can't be followed. "Podcast cannot be added because the server or feed cannot be found."
Thanks!!! We'll try to fix this.