Wikipedia:Reference desk/Archives/Mathematics/2012 February 26

= February 26 =

relating entropy ratchet to stock market fluctuations
suppose that the ones and tens digit of the closing dow jones industrial average each day was a stochastic process. could you explain why it is impossible to use an entropy ratchet type thing to keep getting money out of it? (like maxwell's demon). is it because of broker's fees or is there a fundamental mathematical reason? --80.99.254.208 (talk) 14:57, 26 February 2012 (UTC)
 * you may use this, which I don't understand: http://en.wikipedia.org/wiki/Parrondo%27s_paradox . This is not homework!  Also please bear in mind that the dow jones industrial average is not hte only average: there are a couple that we could combine as with the paradox mentioned.  I would like a general proof or explanation of why this is not possible.  Or is it just broker's fees.  --80.99.254.208 (talk) 14:59, 26 February 2012 (UTC)
 * Could you explain how you would make money out of it? If you explain your algorithm, I expect we can find the flaw in it. In general terms, the market tends to price assets so that there are no arbitrage possibilities (that is, ways of making risk-free profit). If an arbitrage did exist, lots of investors would take advantage of it and that would move the prices until the arbitrage was no longer possible. --Tango (talk) 15:42, 26 February 2012 (UTC)
 * I would like you to supply the winning algorithm, please. (Or else a proof that it could not exist).  --80.99.254.208 (talk) 09:12, 27 February 2012 (UTC)
 * ...? I would like some math here, please. The argument "if it did exist, someone would be using it" is not very mathematical, as by that argument, no mathematician would ever conjecture anything that was provable, since if a proof were possible, someone would have proven it and the mathematician would already know about this proof.   I am asking for some actual math here, please... --80.99.254.208 (talk) 06:49, 28 February 2012 (UTC)

I didn't get an answer about the entropy ratchet. Why can't two stock market indices be treated as the two losing games in Parrondo's paradox? --80.99.254.208 (talk) 09:15, 29 February 2012 (UTC)
 * Someone will generally only volunteer an answer when they feel that they can contribute something worthwhile within their sphere of expertise and they take an interest in the question, and when the question is sensibly framed. In this case, it deals with the specialized area of statistics called game theory, and you have asked a question that would take a thesis to answer.  You could just as well have asked for a mathematical proof of the impossibility of perpetual motion engines, and you would have received little more than "it's inconsistent with scientifically accepted theories of physics".  I suspect you've received as good an answer from Tango as anyone is likely to give.  — Quondum☏✎ 11:11, 29 February 2012 (UTC)
 * I don't think it "takes a thesis to answer" - I already guessed an answer, but didn't want to change anyone's preconceptions by stating it. I thought, though I could be wrong, that at the times that you 'switch' in the quoted paradox, the other game has to actually have a positive expected value on that round: but for a pure stochastic process, there would never be that positive expected value.  But I'm not satisfied with this answer, as stock market indices are fundamentally different from, say, flipping coins.  Flipping coins just doesn't look like the random walk a stock market takes.  So I think there is a better answer, and I bet there are lots of quant finance mathematicians here who could tell me the answer.  I would like a generalized answer.  This is not a thesis type thing but ought to be a fairly straight-forward question for anyone who understands statistics, finance, maxwell's demon (which might not be relevant), and-or the quoted Parrondo's paradox or entropy. --188.6.93.81 (talk) 12:42, 29 February 2012 (UTC)
 * It might also require someone who has a sufficiently accurate mathematical model of the stock market behaviour, which is a tough call. But good luck in finding someone who is willing to take up the challenge.  I don't even see a way to identify a ratchet analogue in the scenario.  I see no way of distinguishing the scenario from uncoupled shares when allowing a pool of cash.  As to the "random walk" of stocks not like coins, if you can quantify the difference, you could in principle exploit that.  — Quondum☏✎ 15:09, 29 February 2012 (UTC)