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Jiro comments on A proposed inefficiency in the Bitcoin markets - Less Wrong
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I have no doubt that a real-life stock can change in a manner similar to a log scale, but if it changed in a manner exactly like a log scale, the company could never fail (sending the value to 0) and it could grow larger than the size of the entire economy.
Given that "it can only grow to a certain size before you exceed the real-life limit" transforms the St. Petersburg paradox from infinite expected value to a small expected value, I would expect to see anyone proposing this model show that such real-life limits don't destroy this model in the same way.
The optimization that I've been linking to- take the derivative with respect to exposure, set it equal to 0- is a 1-step optimization problem. That is, the strategy I'm describing as optimal (Shannon's Demon) is optimal even if there's only one coin flip, and because of the nature of the setup and the log utility function what's optimal for one coin flip is optimal for an arbitrary number of coin flips.