I think we’re disagreeing about terminology here, not anything substantive, so I mostly feel like shrug. But that feels to me like you’re noticing the framework is deficient, stepping outside it, figuring out what’s going on, making some adjustment, and then stepping back in.
I don’t think you can explain why you made that adjustment from inside the framework. Like, how do you explain “multiple correlated bets are similar to one bigger bet” in a framework where
Bets are offered one at a time and resolved instantly
The bets you get offered don’t depend on previous history
It feels to me like a natural modeling choice. To apply simple physics to child-on-swing, model the child as a point mass. To apply Kelly to many highly correlated bets, model them as one large bet. To apply Kelly to many weakly correlated bets, model them as many independent bets. And we also need to make some modeling choice to convert insurance policies to a series of independent bets.
Maybe you’re saying that we need a reason to justify those choices, because bad model choices can give bad results. So we need to “go outside the Kelly framework” to get that justification. If so, I agree.
I think we’re disagreeing about terminology here, not anything substantive, so I mostly feel like shrug. But that feels to me like you’re noticing the framework is deficient, stepping outside it, figuring out what’s going on, making some adjustment, and then stepping back in.
I don’t think you can explain why you made that adjustment from inside the framework. Like, how do you explain “multiple correlated bets are similar to one bigger bet” in a framework where
Bets are offered one at a time and resolved instantly
The bets you get offered don’t depend on previous history
?
It feels to me like a natural modeling choice. To apply simple physics to child-on-swing, model the child as a point mass. To apply Kelly to many highly correlated bets, model them as one large bet. To apply Kelly to many weakly correlated bets, model them as many independent bets. And we also need to make some modeling choice to convert insurance policies to a series of independent bets.
Maybe you’re saying that we need a reason to justify those choices, because bad model choices can give bad results. So we need to “go outside the Kelly framework” to get that justification. If so, I agree.