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gjm comments on A hypothetical question for investors - Less Wrong Discussion
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Nope. And if what you're after is the best long-run result and your utility is anything like logarithmic in wealth, this is exactly what you want.
(Although if Pr(lose everything) is small enough then the observation that you almost always get approximately the expectation in the long run is irrelevant unless the run is infeasibly long. So you might want to truncate your return distributions somehow, if you're prepared to accept a tiny probability of ruin for doing better almost all the time.)
[EDITED to add a missing right-parenthesis.]
Notice that if you have a fixed time horizon the situation changes and you can optimize for how large a probability of ruin should you be prepared to ignore.
That's why I said, in my original comment, "ignoring horizon effects when you know the game will be ending soon" :-).
This doesn't seem right. Let's assume that the stock gives double or nothing, with 51% probability of double. The Kelly Criterion suggests giving 1% of the total payroll in stock. Yes, this neglects the balancing fee. Your argument seems to suggest that we should be all in cash. But the Kelly bet outperforms this.
I don't understand: the situation here is one where your only option is to be all in cash or all in the stock. The Kelly criterion only makes sense when you can choose an arbitrary fraction to be in each.
(And the Kelly criterion amounts to maximizing E(delta log wealth), which is exactly what I'm proposing. If you have to wager your entire bankroll, any gamble with a nonzero chance of bankrupting you has E(delta log wealth) = -infinity and just sitting on your cash is better.)
Ah, I missed that part of the OP. So then I think your argument is correct.