市场有效当且仅当P = NP
Markets are efficient if and only if P = NP
摘要：
我证明，如果市场是弱式有效的，这意味着当前价格完全反映了过去价格中的所有信息，那么P = NP，这意味着每个计算问题的解决方案可以在多项式时间内验证，也可以在多项式时间内解决。我也证明了相反的，通过展示我们如何可以“编程”市场来解决NP完全问题。由于P可能不等于NP，市场可能不是有效的。具体而言，随着时间序列的延长或变得更加频繁，市场变得越来越低效。通过基于数据可用性将超额收益率划分为动量策略的说明证实了这一预测。
英文摘要：
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.
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