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"Markets are efficient if and only if P=NP." http://arxiv.org/abs/1002.2284 A very interesting paper.

Mathematics
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There's some time series analysis in this I think... can anyone recommend any good texts on that stuff?
unsolved problems?

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Well, P=NP is naturally an unsolved problem. This paper is making the assumption that it is the case, though.
Was about to say, P=NP is an unsolved problem..
Abstract: "I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can "program" the market to solve NP-complete problems. Since P probably does not equal NP, markets are probably not efficient. Specifically, markets become increasingly inefficient as the time series lengthens or becomes more frequent. An illustration by way of partitioning the excess returns to momentum strategies based on data availability confirms this prediction."
this is too heavy for me disrete (abstract) math
Looking through it I can't find anything about time series analysis, despite what the abstract might suggest. Kind of handwaved as irrelevant.

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