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Mr. Soros in his books talked about principles which are not used by today's financial mathematics — namely reflexivity of all actions on the market. Simply it can be given by following: expectations of traders are based on the news and historical prices. They trade based on their expectations and hence influence prices which then influence expectations on the next "turn". I have never met an implementation of these ideas in the scientific framework. Have you? If yes, please give me a reference.

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I think most would refer to Soros's "reflexivity" as "mean reversion". I think his point is that there are frictions that delay mean reversion (i.e., the market can bear some mis-pricing before reverting back to the correct level). –  Richard Herron Apr 5 '11 at 9:42
@richardh That's funny, because I would call it "momentum". –  Shane Apr 16 '11 at 23:00
@shane -- I wrestle with the distinction between momentum and mean reversion; they seem to be two sides of the same coin. One month's winners are the next's losers (short run reversal), $j$-month winners win for the next $k$ months after you skip a week (momentum), and stocks that win for 36-60 months lose for the next 24 or so (long run reversal). And vice versa. –  Richard Herron Apr 17 '11 at 16:51
are j and k fixed in your example? Otherwise this is just the description of a random walk. –  RockScience Apr 18 '11 at 3:17
why did this MARKED as answered question popped up again? I have value to add I believe but the question is marked answered... –  Matt Wolf Dec 9 '12 at 10:16
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5 Answers

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Keynes introduced this idea in the notion of a Keynesian Beauty contest: http://en.wikipedia.org/wiki/Keynesian_beauty_contest

Anyone who uses a rolling window regression where the parameters and/or parameter estimates are re-fitted periodically are implicitly accounting for this reflexivity (i.e. the market's changing behavior as agents respond and adapt to each others actions)

With respect to a scientific-framework, agent-based modeling is something that fits the bill and also game theory: http://en.wikipedia.org/wiki/Agent-based_model

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I very much agree that game theory is the relevant discipline. In particular, the subfield of learning in games, also called evolutionary game theory. –  MichaelJ Dec 9 '12 at 6:58
@Quant Guy: whops it seems that I downvoted by error, I want to upvote instead (although I disagree on some points), could you please edit to unlock vote changes? Thanks! –  Quartz May 31 '13 at 10:29
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The answers above are good, but I suspect they will be unsatisfactory if you are looking for implementations that are successful in practice. The sort of bottom-up analysis championed by Soros is very difficult to carry out in a rigorous, quantitative manner. This is true very generally, not just in finance. There are certainly models of financial markets that explicitly consider beliefs and actions of individual market participants (see game theory), but these always rely on extreme oversimplifications of actual human cognition and behavior.

On the other hand, many seem to be able to develop a good intuitive sense for what sort of beliefs and biases are driving the behavior of financial market participants and exploit this knowledge. Soros is often counted among their ranks. Although this approach may be sophisticated, it is usually not considered quantitative. Soros often claims that he looks for a sort of "turning point" where market participants realize the flaws in their beliefs. This is in contrast with most quantitative models that implicitly assume that whatever structure is observed in the data will persist long enough for a profit to be extracted.

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There are "quantitative" indicators for that kind of strategies still, like market sentiment... I know you didn't mean there weren't but it's just to emphasize it's not only about the trader's feeling, he uses quantitative tools. –  SRKX Dec 12 '12 at 18:44
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This paper by Filimonov and Sornette might be interesting or useful to you. I've only read about the first third, but I thought the model was pretty cool. The model for price changes is a self-exciting Poisson process: there is an exogenous factor modeling the "real" price changes, and then there is a feedback mechanism where the overall arrival rate is an exponentially weighted average of recent arrivals. The paper is available here. If you go through it all, would welcome your thoughts.

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That's indeed interesting, a very recent paper - thanks! –  Ilya Jun 1 '13 at 12:12
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Sure it is used in non-linear dynamics. What is not used is that this non-linearity is caused by huge operators who cause the deviation from Normal Law delaying the reversion to the mean. This is just common sense and mathematically logics when you go straight to Normal Law premisces: all samples must have about the same weight and being independant. Clearly these premisces are hugely violated in Stock Market.

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I havent seen much implementing reflexivity in practice in a comprehensive way. Of course there are small steps in that direction, but no general framework yet.

To comment on answers above: incorporating updates of information is not reflexivity; reflexivity is about taking into account the effect of your own actions while chosing them (jointly with those of other market participants, sure), that is ex ante, not ex post. Also momentum and mean reversion need not have anything to do with reflexivity.

Even the modeling of market impact in algo trading, which should be the application par excellance of reflexivity, is still done in a kind of traditional "blind" way: ex post statistics of impact are taken and then the forecasting model is used to optimize strategies... Reflexivity in algo trading would be best applied to avoiding stop loss crashes, which is currently not yet done afaik. But sure market impact modeling goes a little bit towards reflexivity in a short term sense.

Stochastic control is one area where some reflexivity is indeed present by definition. And sure game theory, but that's not used much in practice.

Something might also be found in the bubble dynamics literature, but I'm not familiar with it. Agent modeling is surely interesting per se, but in its current state is far from even scratching the surface of that topic, and the main research stream doesnt touch reflexivity at all.

More on control theory (w/o stochasticity) which is already pertinent (see also dynamic programming). It deals with the response dynamics of a system to different inputs and how to best plan strategies. E.g. it is used in engineering to study and prevent oscillations. Oscillations are the typical problem arising when no control techniques are used (as seen in economic cycles, bubbles etc...): a target is aimed at, a steering parameter is directed towards that but the actual response of the system is not linear so the steering needs to be corrected, but then the correction itself must be called back with time yet still the dynamics leads away in the other direction, so one has to steer again in the original direction, and so on in an endless cycle... E.g. in algo trading of course your target is the quoted price, but you must adjust it to take into account market impact, which however is not given but depends itself on the your target and strategy generating some circularity. Control theory iirc is applied in pricing of americans for the exercise strategy, and all similar problems, although it's overkill since there's much more to it. Here some examples in finance. (Definitely people at the FED should take a course in control theory, before they start messing that way with the world economy. What will happen with inflation is a classic case of control myopia where they're oversteering without noticing it before it's too late. Here some examples in economics.)

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+1 Stochastic control is one area where some reflexivity is indeed present by definition. - can you be more specific here? –  Ilya May 31 '13 at 12:31
@Ilya: sure, I edited the answer because of lack of space here. –  Quartz May 31 '13 at 13:03
Well, I am familiar with principles of the stochastic optimal control and dynamic programming. Surely, you can incorporate the reflexivity there - my question was rather on how to incorporate it in a practically meaningful way, that's why I've whether there are some financial models known that involve reflexivity as per Soros. –  Ilya Jun 3 '13 at 9:30
Whops hadn't noticed your field... then please keep us updated if you find more on this! –  Quartz Jun 4 '13 at 10:46
NP, I just updated my description recently so it might have not been there before –  Ilya Jun 4 '13 at 11:03
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