Markets are efficient if and only if P = NP
Sigh. Cheers, RAH ---------- http://arxiv1.library.cornell.edu/abs/1002.2284arXiv.org > q-fin > arXiv:1002.2284 Quantitative Finance > General Finance Markets are efficient if and only if P = NP Philip Maymin (Submitted on 11 Feb 2010) 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. Subjects: General Finance (q-fin.GN); Computational Complexity (cs.CC) Cite as: arXiv:1002.2284v1 [q-fin.GN] Submission history From: Philip Maymin [view email] [v1] Thu, 11 Feb 2010 05:56:16 GMT (46kb,X) Which authors of this paper are endorsers? Link back to: arXiv, form interface, contact.
Chuckle. He would better spend his time analyzing if "money out of nothing" = something.... and what its effects on the resultant so-called "market" is. Cheers, ---Venkat. http://www.global-settlement.org http://www.rayservers.com/blog http://www.rayservers.com/blog/redeclaration-of-the-american-republic On 02/23/10 11:10, R.A. Hettinga wrote:
Sigh.
Cheers, RAH ----------
http://arxiv1.library.cornell.edu/abs/1002.2284arXiv.org > q-fin > arXiv:1002.2284
Quantitative Finance > General Finance Markets are efficient if and only if P = NP Philip Maymin (Submitted on 11 Feb 2010) 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. Subjects: General Finance (q-fin.GN); Computational Complexity (cs.CC) Cite as: arXiv:1002.2284v1 [q-fin.GN] Submission history From: Philip Maymin [view email] [v1] Thu, 11 Feb 2010 05:56:16 GMT (46kb,X) Which authors of this paper are endorsers? Link back to: arXiv, form interface, contact.
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From: "Rayservers"
Chuckle. He would better spend his time analyzing if "money out of nothing" = something.... and what its effects on the resultant so-called "market" is.
I disagree, its actually useful, in a particularly odd way. The profitability of hedge funds says that the markets are not efficient (one of their founding principles). So the inability of a massive multiprocessing system to build proper market efficiency indicates that no one currently has a solution to prove P=NP. There is also far more money in economic research than in algorithmic research, so anyone who manages to bring the market to being efficient will in fact have proven P=NP long before the algorithm is known. From a security standpoint this is extremely valuable information. Maybe Maymin should apply the same processes and become a hedge fund manager, they make a lot more money than mere engineers. Joe
On Tue, Feb 23, 2010 at 5:27 AM, Joseph Ashwood
... the inability of a massive multiprocessing system to build proper market efficiency indicates that no one currently has a solution to prove P=NP.
correlation != causation also, the strong-form efficiency present in such an analysis fails in the face of biased and flawed real-world market actors. cognitive and informational biases render such approaches masturbatory at best.
There is also far more money in economic research than in algorithmic research...
leveraging economic research interest to fund algorithmic research is a clever approach to funding perhaps.. :)
... Maybe Maymin should apply the same processes and become a hedge fund manager, they make a lot more money than mere engineers.
until they blow up*. the quant meltdown brought such computational hubris back to earth... (Renaissance Institutional Equities Fund was down 6% at the start of this year. and 2009 should have been a good year for a hedge!) * nassim talib == the man he, by the way, recognized inherent market instability as an opportunity. the Universa fund he advises made returns of 65% to 115% in oct 2008 via his "black swan protection protocol.
participants (4)
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coderman -
Joseph Ashwood -
R.A. Hettinga -
Rayservers