It’s important that we can derive Kelly that way, but if that were the only derivation, it would not be so interesting. It begs the question: why log wealth?
The derivation that does something interesting to pin down Kelly in particular is the one where we take the limit in iterations.
+1. It’s important to understand that log(money) is the RESULT that Kelly showed, not an assumption he made. If you start with it as an assumption, you’re not “deriving” the Kelly equation, you’re just calculating it.
This result is what makes logarithmic utility so attractive as an assumption in OTHER kinds of utility modeling.
It’s important that we can derive Kelly that way, but if that were the only derivation, it would not be so interesting. It begs the question: why log wealth?
The derivation that does something interesting to pin down Kelly in particular is the one where we take the limit in iterations.
+1. It’s important to understand that log(money) is the RESULT that Kelly showed, not an assumption he made. If you start with it as an assumption, you’re not “deriving” the Kelly equation, you’re just calculating it.
This result is what makes logarithmic utility so attractive as an assumption in OTHER kinds of utility modeling.