Thank you for the link. you say, "do not expect to be correct" but the abstract of the paper you linked says "Since P probably does not equal NP, markets are probably not efficient". do you agree with the paper?
> For simplicity but without loss of generality, assume there are n past price changes, each of which is either UP (1) or DOWN (0). How many possible trading strategies are there? Suppose we allow a strategy to either be long, short, or neutral to the market. Then the list of all possible strategies includes the strategy which would have been always neutral, the ones that would have been always neutral but for the last day when it would have been either long or short, and so on. In other words, there are three possibilities for each of the n past price changes; there are 3^n possible strategies.
The number of possible n-move histories is 2^n, not n. That means there are 3^(2^n) possible strategies. Nondeterministically searching that space in polynomial time does not work. The claim that a strategy could be verified in O(n) time is dubious as well since the size of a full description of a strategy is (in the worst case) exponential in the length of history it considers. So their claim that finding a technical strategy which performs well in backtesting is in NP is not proven.
They repeat the same error later:
> there are 2^(t + 1) possible strategies (because every possible strategy is a mapping from 2^t different possible sequences of 1’s and 0’s of length t into two possible choices, LONG or OUT)
There are other issues, like assuming a strategy that backtests well will continue performing well in the future.
https://news.ycombinator.com/item?id=19722455
Any thoughts?
"Markets are provably not efficient because xyz" is much harder to agree with, especially given that paper, since it's the same as saying you've actually proven that P!=NP and thus requires an extraordinary proof.
You're claiming to have a solid proof. Just because someone agrees that your result is likely correct, that doesn't mean they agree with your proof.
if the paper is flawed, nothing follows from it, there's no reason to spend time on it except to understand its flaws. Then it's just another crank paper, besides and unrelated to mine.