i.e. E[log(X)], E[log(Y)] < E[log(Z)] does not imply that E[log((X+Y)/2)] < E[log(Z)]
Let me see if I can turn this into a proof either way
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OK so I think:
1) is wrong given his assumptions
2) if you *also* assume that there aren't two pots which have coins with *exactly* the same growth rate, is right given his assumptions
3) his assumptions are stupid
4) given good assumptions, he's wrong
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If there are two pots with the same growth rate, and you can’t rebalance between them, you think you can beat the growth rate?
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And the objectionable assumption that I’m making is the infinite time horizon, right?
And I guess the assumption “I prefer A to B if A outperforms B with probability 1” but that seems really hard to object to (apart from objecting to the infinite time horizon)
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nope, there are a lot of bad assumptions!
1) infinite time horizon
2) the prob dist of the coins: your model relies on the claim that with p --> 1, ETH > $999999999999999 eventually
3) that you can't rebalance
4) that you can't choose a better way to trade
...cont'd
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5) that you assign prob 0 to blowing out to ~$0 and staying there with an AMM
6) that you lose only epsilon to each arb
7) (that you are log-maxing but while I think that's wrong it's not *stupid*)
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8) and, yes, the thing you said it's hard to object to.
you still haven't responded to
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Fair, I didn’t mean every assumption in the post about rebalancing portfolio growth, just in this separate hypo about pots. But I see why you think it’s an unrealistic scenario.
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wait but this separate hypo has to inherit all the stupid assumptions from the post about growth or else the hypo is wrong!
No? The hypo is just about pots with some expected log growth. The pots are black boxes. No mention of rebalancing or anything
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At any rate this hypo is definitely a tangent—the reason I am harping on it is because you and Arthur said that I was unambiguously wrong on the math
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