In the 90's there was a multitude of new quantitative financial theories conjured up in order to construct models that would outperform the market. One of which was the application of Chaos theory to financial markets. In short, small actions could lead to major changes in financial markets. Figuring out what these complex interdependencies in markets are, would yield models that could be used to predict how markets change.My question is, is the application of Chaos theory to financial markets dead? Are still exploring this field or has it died down?

"chaos theory" was very popular in 90s everywhere, not just finance. it's not actually a theory to me. i dont know what's "chaos theory". i read a few books in 90s, it was more like a philosophy. it's like trying to build a theory on just one concept like "uncertainty principle" then stick a bunch of loosely related equations to it, and try to apply to everything. it didn't work. the only place where it works is thermodynamics.

You might model a market as non-linear system that will produce sim results that are deterministic ... bcoz you used deterministic input variables. But input variables are rather random eg order arrival times (inhomogenous time scale!), varying order specs etc. (in realtime horizons agents decide independent from each other bcz it s not possible all agents know the decisions of each other while deciding; the complete information assumption would contradict to the independence condition?!) Thus the non-linear system produce random points eg prices series -- random in, random out.

I agree with jawabeen, ChTh is an awareness-creating name for the theory of complex, nonlinear systems.What it has in common: systems which get complex behaviour from the massive application of simple "rules". You could think of genetic or evolutionary algorithms as generic approaches for (global) optimization (has applications in qf).(in a detail, in Mathematica they do random number generation with Stephen's NKS (cellular automata)). Data mining and machine learning use such approaches.Such theories might get into a renaissance with the availability of massive data (in the petabyte age).(just one example: if you search for more complex "correlation" in market segments, you could create Self Organizing Maps (SOM)).

chaos theory was hot in the days before everyone had fancy desk top computers that could crank out the fanciest colorful chaos pictures in seconds. now chaos theory is as dead as DOS.

I thought Chaos theory was a trance group: oh sorry that is Kaos Theory.Anyway in reality isn't it Non-linear dynamics to those in the know, other than that it is a media term.

QuoteOriginally posted by: KackToodleschaos theory was hot in the days before everyone had fancy desk top computers that could crank out the fanciest colorful chaos pictures in seconds. now chaos theory is as dead as DOS. I dont think so.There are in finance some current investigation done on stock modelling using some familly of functions (Weierstrass related series) and others of the kind. I remember seeing a reference a few weeks ago : not sure where now.As for chaos theory it was in the 90's a "vulgarisation" term for the study of dynamical systems, which is an area that has been very active from the 60´s (and even before...) to now. I am a former researcher in non uniformly hyperbolic systems (NUHS) and holomorphic dynamics, if people ask me what I used to do : chaos theory is the answer.It is actually not so far from the truth in particular in NUHS where we were concerned about stability of ergodicity (which in short math terms means no invariant sets of positive measure, or even simpler : lotsa chaos )

QuoteOriginally posted by: BourbaQuoteOriginally posted by: KackToodleschaos theory was hot in the days before everyone had fancy desk top computers that could crank out the fanciest colorful chaos pictures in seconds. now chaos theory is as dead as DOS. I dont think so.There are in finance some current investigation done on stock modelling using some familly of functions (Weierstrass related series) and others of the kind. I remember seeing a reference a few weeks ago : not sure where now.As for chaos theory it was in the 90's a "vulgarisation" term for the study of dynamical systems, which is an area that has been very active from the 60´s (and even before...) to now. I am a former researcher in non uniformly hyperbolic systems (NUHS) and holomorphic dynamics, if people ask me what I used to do : chaos theory is the answer.It is actually not so far from the truth in particular in NUHS where we were concerned about stability of ergodicity (which in short math terms means no invariant sets of positive measure, or even simpler : lotsa chaos )perhaps what you wanted to say is chaos theory is not dead - but that's probably different from chaos theory in finance being dead ...

if fundamental research is going on a subject then it is definitely not dead... it just means that chaos theory's applications in Finance are in a vegetative state ;PAnyways I have even heard of some insane souls trying to apply partially hyperbolic systems to statistical modelling applied to finance : some people really are masochists.so chaos theory applied to finance is not dead... but it might take a while for it to wake up ... You see the main problem is that real (I mean "pure" as opposed to "applied") mathematicians could not care less about a trivial matter as finance or mathematical finance , and real (I still mean "pure") chaos theory is everything but applied or "applyable" : people will show you nice pictures of the Mandelbrot set but the math behind those is unreachable even for Mandelbrot (why the set was not called the Douady set is a mystery to me, well, he got the rabbit anyways).Bourba (ki)

It is certainly not dead. We should not probably to think about this as a universal theory which solves everything, but it can help. For example, if you have some agent based model, where you need stochasticity somewhere, you can replace it by chaotic generators and you will be surprised how different results you get. Questin is, whether these different result will be closer to reality you observe... and they sometimes seems to be closer, thus Chaos is not certainly dead in economics. One just have to use it carefully without too much hope.

was chaos theory ever alive?!

Don't be so sarcastic;-) The life of the Chaos theory seems to me as strong as the linearization in standard macroeconomics models...

QuoteOriginally posted by: hanssDon't be so sarcastic;-) The life of the Chaos theory seems to me as strong as the linearization in standard macroeconomics models... flip through a regular issue of journal of finance. how many articles use linearized models versus how many mention chaos theory?

QuoteOriginally posted by: deepvalueQuoteOriginally posted by: hanssDon't be so sarcastic;-) The life of the Chaos theory seems to me as strong as the linearization in standard macroeconomics models... flip through a regular issue of journal of finance. how many articles use linearized models versus how many mention chaos theory?Ask yourself : why linearizations ? 1)Because they work as a first order approximation to a certain modelization of reality 2)Because they are easier to computeWe are making three strong assumptions here (that our model works, that it is mainly of the first order and that since we can compute and calibrate it to reality then it is valid).What is really behind this view of the world is that we know the world is complex or even chaotic BUT we assume the laws dictating its evolution are simple. And this is actually a valid way to study a chaotic system (since it works).Another equivalent way to study the same problem is to say : the world is simple, there are a finite number of relevant variables that allows us to understand its evolution BUT its evolution laws are extremely complex. As I see it, this is were chaos theory really stands : problem is, as of today you cant get computational results from this, only in some particular cases and most of the results concern the classification of such chaotic dynamics.So yeah, you wont see much besides linearizations, still does not mean chaos theory is dead

Brian Arthur Santa Fe Institute (of Complex Systems)