From the paper: "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.
However, there has been no proof that there does not exist some algorithm that can determine satisfiability in polynomial time. If such an algorithm were found, then we would have that P = NP. If a proof is discovered that no such algorithm exists, then we would have that P ≠ NP.
Just as most people in the field of finance believe markets are at least weak-form efficient,
most computer scientists believe P ≠ NP. Gasarch (2002) reports that of 100 respondents to his
poll of various theorists who are “people whose opinions can be taken seriously,” the majority
thought the ultimate resolution to the question would be that P ≠ NP; only 9 percent thought
the ultimate resolution would be that P = NP.
The majority of financial academics believe in weak form efficiency and the majority of
computer scientists believe that P ≠ NP. The result of this paper is that they cannot both be
right: either P = NP and the markets are weakly efficient, or P ≠ NP and the markets are not
weakly efficient. "
From the paper: "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.
However, there has been no proof that there does not exist some algorithm that can determine satisfiability in polynomial time. If such an algorithm were found, then we would have that P = NP. If a proof is discovered that no such algorithm exists, then we would have that P ≠ NP. Just as most people in the field of finance believe markets are at least weak-form efficient, most computer scientists believe P ≠ NP. Gasarch (2002) reports that of 100 respondents to his poll of various theorists who are “people whose opinions can be taken seriously,” the majority thought the ultimate resolution to the question would be that P ≠ NP; only 9 percent thought the ultimate resolution would be that P = NP. The majority of financial academics believe in weak form efficiency and the majority of computer scientists believe that P ≠ NP. The result of this paper is that they cannot both be right: either P = NP and the markets are weakly efficient, or P ≠ NP and the markets are not weakly efficient. "