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The solution in the post is wrong, or my interpretation of it?
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A bit of a definitional issue -- the interpretation is mostly wrong; the solution is the correct solution to *a* question but not to *the right question to be asking*
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It's trying to maximize EV[log(money)] instead of EV[money].
This is probably wrong in and of itself as an assumption to make.
But if you *do* want to make that assumption, then e.g. you have to consider all of your assets that don't have anything to do with the pool.
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So:
1) it's not literally *wrong* in that it doesn't make a math error
2) I disagree in general that Kelly is the right way for people to bet because I disagree with its assumptions
3) neither 1/2 are necessary for my argument: Kelly only works if you consider *all* your money
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There are other problematic assumptions snuck in here, e.g.
a) the paper assumes that you can only do one or the other forever and can't ever take profit if you don't use an AMM
b) the paper assumes that exponential increase in valuation can go on forever
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E.g. see what happens to the math if you assume:
a) The person is only using 25% of their money in this particular USD/coin pair and 75% outside of the system
b) you only expand out ~10 years
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You might be surprised here. Similar results should hold at least for different utility functions and portfolio compositions. Do you have a proof to the contrary?
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well, e.g. if your utility function is linear then you never rebalance
Even if your utility function is linear you should rebalance. You will almost surely have higher utility in the long run if you do
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So I think that you should probably self-reflect a little bit here and ask yourself what your priors are on who's right on this particular subquestion.
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Right, sure. Would you be willing to concede the result in all but the linear case?
Concretely, I believe there's a similar result that holds even for "more linear" objective functions than log(X).
(btw growth-optimality exists regardless of the functional form for utility)
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And it is not actually true for the linear case, at least if it isn’t your last chance to use your capital to make more money ever
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