I think one thing a lot of this arguments for Kelly Betting are missing: we already know that utility is approximately logarithmic with respect to money.
So if Kelly is maximizing the expected value of log(utility), doesn’t that mean it should be maximizing the expected value of log(log(money)) instead of log(money)? 🤔
Correct, but the arguments given in this post for the Kelly bet are really about utility, not money. So if you believe that you should Kelly bet utility, that does not mean maximizing E(log(money)), it means maximizing E(log(log(money)). The arguments would need to focus on money specifically if they want to argue guess maximizing E(log(money)).
I think one thing a lot of this arguments for Kelly Betting are missing: we already know that utility is approximately logarithmic with respect to money.
So if Kelly is maximizing the expected value of log(utility), doesn’t that mean it should be maximizing the expected value of log(log(money)) instead of log(money)? 🤔
I believe Kelly maximizes E(log(money)), no?
Correct, but the arguments given in this post for the Kelly bet are really about utility, not money. So if you believe that you should Kelly bet utility, that does not mean maximizing E(log(money)), it means maximizing E(log(log(money)). The arguments would need to focus on money specifically if they want to argue guess maximizing E(log(money)).