"The original meaning is that a gambler who raises his bet to a fixed fraction of bankroll when he wins, but does not reduce it when he loses, will eventually go broke, even if he has a positive expected value on each bet."

Yep, that is correct, but the kelly criterion requires fractional betting, which at some point in the real world is not possible, especially with options.

This is because there is a limited amount of options you can sell/purchase, so the fractional bet will always decrease as your bankroll increases. And there is also a floor where you cannot purchase below if your bankroll falls below (though your investors would have wiped you out by than).

That is suboptimal