The basic idea is that given a financial time series of N periods with three states (up, neutral, or down) there are 3^N possible "strategies" to test, which is an NP problem.
This doesn't seem right. It's completely atheoretical and ignores the market or asset structure. The question is not how many strategies there are, but how hard is it to compute the optimal price. Basic economic theory often can be used to derive the optimal price as a simple function of information (data).
There may an argument that markets are inefficient that follows an NP=P style argument, but I suspect it would require a specific market structure, such as a set of agents that can only communicate via a sparse network.
Abstract: I prove that if markets are 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.
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This is basically an attack on the efficient market hypothesis - i.e., that markets price in all available information and market moves over the long term accurately reflect the best consensus guess as to the future of a particular company. For background, see Wikipedia:http://en.wikipedia.org/wiki/Efficient-market_hypothesis
What I see as the interesting part of this paper is way in which the author uses market mechanisms - a trading strategy - to test problems as being in the P or NP space, basically equating the market to a type of computational machine. He argues that if the EMF is true, then a properly set up experiment should be able to come up with a solution to an NP problem in polynomial time (implying P=NP).
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[ 6.5 ms ] story [ 25.7 ms ] threadThis doesn't seem right. It's completely atheoretical and ignores the market or asset structure. The question is not how many strategies there are, but how hard is it to compute the optimal price. Basic economic theory often can be used to derive the optimal price as a simple function of information (data).
There may an argument that markets are inefficient that follows an NP=P style argument, but I suspect it would require a specific market structure, such as a set of agents that can only communicate via a sparse network.
===
This is basically an attack on the efficient market hypothesis - i.e., that markets price in all available information and market moves over the long term accurately reflect the best consensus guess as to the future of a particular company. For background, see Wikipedia:http://en.wikipedia.org/wiki/Efficient-market_hypothesis
What I see as the interesting part of this paper is way in which the author uses market mechanisms - a trading strategy - to test problems as being in the P or NP space, basically equating the market to a type of computational machine. He argues that if the EMF is true, then a properly set up experiment should be able to come up with a solution to an NP problem in polynomial time (implying P=NP).