> > Jose makes a good point though—if the author was trying to disprove > > efficient market hypothesis—then proving the weakest form to be false > > implies all forms are false. > > But, technically, the author didn't prove EMH false -- he outlined an > equivalence between EMH and the knapsack problem.
If one can show that the markets are probably not weak efficient then one can state that "the markets are probably not efficient" (in any form) as the author states in the abstract of his paper. > In other words if we could solve problems whose complexity grows > exponentially, then EMH would be true. Since we can't, we can at least > classify EMH as not always being useful in the general case. Clarify why "Since we can't," then "we can at least classify EMH as not always being useful in the general case" and what your statement means, in particular, "being useful" (if you can). > Actually, he was talking about offering contract terms whose conditions > would be met by the problem solution. > > But his point was that it's not reasonable to expect that the market would > be able to solve such things. > So far *if* the (presumably bug-free) program would fail to solve 3-SAT problems in La La Land then some markets would not be efficient in the strong or semi-strong sense. In other words, so far, the alleged strong or semi-strong inefficiency *might* only be falsified in Lala Land. > > In mathematics, one way to disprove a theorem is to show that is leads to a contradiction—thus the examples I mentioned that contradict EMH. > > Yes. Maybe I am completely mistaken and you both have just shown us an irrefutable proof that the markets are inefficient and the paper undoubtedly proves that, Markets are efficient if and only if P = NP then you have both proved P ≠ NP; the only remaining question is how will you both split the $1,000,000.00? On Fri, Aug 23, 2019 at 1:14 PM Raul Miller <[email protected]> wrote: > > On Thu, Aug 22, 2019 at 8:49 PM Donna Y <[email protected]> wrote: > > > 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. > > > > This statement baffled me because N=NP is an unproven theorem—one of > > the millennium problems with a reward of $1 million for proving or > > disproving. Nowhere in the paper does he show any equivalence between > > N=NP and efficient markets. > > To understand the equivalence he's drawing between P=NP and efficient > markets you have to understand the P=NP concepts. (He uses concepts > related to the knapsack problems in market contexts to illustrate the > consequences.) > > > The author seems unaware that in mathematics statements cannot be > > both True and False (Even outside mathematics unless I guess you get > > Kelly Ann Conway working for you.) > > True, False or Undecidable from the given axioms. See also: Godel's > incompleteness theorem. > > Or, if you prefer, consider also paradoxes such as: "This statement is false". > > > Jose makes a good point though—if the author was trying to disprove > > efficient market hypothesis—then proving the weakest form to be false > > implies all forms are false. > > But, technically, the author didn't prove EMH false -- he outlined an > equivalence between EMH and the knapsack problem. > > In other words if we could solve problems whose complexity grows > exponentially, then EMH would be true. Since we can't, we can at least > classify EMH as not always being useful in the general case. > > > The author speaks of programming the market to solve NP-complete > > problems. This is also nonsense because the market is busy doing > > other things and would not be controlled by some sort of program on > > demand. Perhaps there is some kind of simulator that could be > > programmed in the sense of an analogue computer to solve problems > > but basically as stated by the author it is nonsense. > > Actually, he was talking about offering contract terms whose conditions > would be met by the problem solution. > > But his point was that it's not reasonable to expect that the market would > be able to solve such things. > > In other words, you're restating his case for why we should not treat > the market as efficient. We could take "busy doing other things" as > a statement of inefficiency (for general case issues). > > > In mathematics, one way to disprove a theorem is to show that is leads to a contradiction—thus the examples I mentioned that contradict EMH. > > Yes. > > Thanks, > > -- > Raul > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
