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Markets are Efficient if and Only if P = NP

Philip Maymin

Vantage Sports; University of Bridgeport - School of Business

February 28, 2011

Algorithmic Finance, Vol. 1, No. 1, 2011
NYU Poly Research Paper

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.

Number of Pages in PDF File: 12

Keywords: algorithmic finance, efficiency, complexity, computation, P, NP

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Date posted: March 1, 2011  

Suggested Citation

Maymin, Philip, Markets are Efficient if and Only if P = NP (February 28, 2011). Algorithmic Finance, Vol. 1, No. 1, 2011; NYU Poly Research Paper. Available at SSRN: http://ssrn.com/abstract=1773169

Contact Information

Philip Maymin (Contact Author)
Vantage Sports ( email )
United States
University of Bridgeport - School of Business ( email )
126 Park Avenue
Bridgeport, CT 06601
United States
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