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Jun 1, 2013 at 14:49 comment added Alexander Chervov Steven trend plus noise model is approximation can be used to catch trends. There is no model which can be used universally.
Jun 1, 2013 at 13:30 comment added Steven Landsburg Joel: There are two reasons to be skeptical of the "trend plus noise" model, neither of them strictly mathematical. First, it's almost impossible to incorporate this model into an equilibrium model in which profit-maximizing traders respond to a price process and thereby change that process. (More prosaically, this model allows for unexploited profit opportunities, whereas we ordinarily assume that unexploited profit opportuntities lead to trading behavior that causes those opportunitites to vanish.) The second reason is the empirical evidence from real world financial assets.
Jun 1, 2013 at 8:34 comment added Alexander Chervov @fedja " the conjecture is, indeed, true for every symmetric distribution." please can you say more on that ? I would accept answer proving it. I am very interested.
Jun 1, 2013 at 4:24 comment added fedja As to the original question, the conjecture is, indeed, true for every symmetric distribution. I'm not sure how practical it is to bet on the stock movements according to that model, but gasoline prices seem to follow a law like that lately, so one can try to optimize the average fuel cost and to see if there is a noticeable advantage compared to the usual "refuel when empty" strategy. The extra difficulty there is that while you are fine waiting with the stock, you cannot wait too long between gas tank refills.
Jun 1, 2013 at 1:31 comment added Joel David Hamkins Given the OP's trend+noise idea, do you have an argument for why prices should be modeled as price changes, rather than prices?
May 31, 2013 at 19:22 comment added Alexander Chervov Thank you for your comments, it helps me to improve (hopefully) the question. I sincerely hope you will modify yours answer accordingly.
May 31, 2013 at 16:36 history edited Steven Landsburg CC BY-SA 3.0
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May 31, 2013 at 15:53 history answered Steven Landsburg CC BY-SA 3.0