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Markets are efficient if and only if P=NP

Author

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  • Maymin, Philip

    (NYU-Polytechnic Institute, NY, USA)

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.

Suggested Citation

  • Maymin, Philip, 2011. "Markets are efficient if and only if P=NP," Algorithmic Finance, IOS Press, vol. 1(1), pages 1-11.
    • Handle: RePEc:ris:iosalg:0001
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    Cited by:

    1. Jonathan Carrero & Ismael Rodríguez & Fernando Rubio, 2021. "On the Hardness of Lying under Egalitarian Social Welfare," Mathematics, MDPI, vol. 9(14), pages 1-15, July.
    2. Rosser, J. Barkley & Rosser, Marina V., 2023. "The Bielefeld School of economics, Post Keynesian economics, and dynamic complexity," Journal of Economic Behavior & Organization, Elsevier, vol. 212(C), pages 454-465.
    3. Philip Z. MAYMIN, 2018. "The Conventional Past, Behavioral Present, and Algorithmic Future of Risk and Finance," Finante - provocarile viitorului (Finance - Challenges of the Future), University of Craiova, Faculty of Economics and Business Administration, vol. 1(20), pages 74-84, November.
    4. Wolfgang Kuhle, 2016. "An Equilibrium Model with Computationally Constrained Agents," Papers 1611.01771, arXiv.org.

    More about this item

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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