From: John Conover <john@email.johncon.com>
Subject: forwarded message from Blake LeBaron
Date: 16 Oct 2000 06:43:29 -0000
There was a discussion last week in sci.econ.research about stochastic
systems. Arijit Mukherji had some questions about the state of the
art, and I replied with references to Blake LeBaron, et al.
The attached is an update from LeBaron on his recent research, (and a
URL,) in NLDS, (Non-Linear Dynamical Systems, e.g., chaotic,) theory.
FYI ...
John
BTW, although NLDS applications to financial markets are promising,
all the researchers are sceptical about the applicability of the
current state of the art to production techniques-the application of
NLDS is in its infancy. LeBaron is one of the leaders, and has a
working relationship with the others.
Although stochastic methods tend to dominate production methodologies
used in financial markets, (like Black-Scholes, for example,) and work
well empirically, there are abstract theoretical issues as pointed out
in the attached-it is very difficult at this time to use scientific
induction to offer a formal argument as to why a financial system
exhibits the stochastic characteristics it does, and how those
characteristics relate to microeconomic phenomena, (like relating
utility issues in a multi-agent system to the observed stochastics.)
Its a formidable ambition.
As a side bar, most systems that are significant in a society are
complex, and in only a few have the micro and macro phenomena ever
been related theoretically, (the weather being one-where stochastic
techniques still prevail in production operations do to the difficulty
of working with formal NDLS models; in point of fact, in the temperate
regions of the planet, just saying that the weather will be tomorrow
what it was today will produce a forecast that has a success rate just
about equal to the meteorologists using NDLS models.)
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From: Blake LeBaron <blebaron@brandeis.edu>
Subject: Re: applied fractals?
Date: Fri, 13 Oct 2000 05:29:16 GMT
Newsgroups: sci.econ,sci.econ.research
conover@rahul.net wrote:
>
> Arijit Mukherji writes:
> >
> > Secondly, if the structure of the model is unknown, and is estimated by some
> > agents who do such a model (in a completely theoretical world, not the real
> > world) does this lead to a model of boundedly rational traders, discovering
> > the structure of the economy, and what are the predictions of asset pricing
> > from such a theoretical model? If we think of traders as optimizing within
> > this framework, how do we generate the objective functions that they
> > maximize and the inferences they draw from prices in a consistent
> > theoretical framework? What restrictions if any does that impose on the
> > data? Since we know there are people who spend vast sums on technical
> > analysis and data mining in order to find returns that are superior to what
> > they believe to be a misspecified theoretical model, can one develop a model
> > that generates them? I know there is some old stuff by Shleifer and Summers
> > et al from the late 80s, but they don't really have a full fledged model.
> > Some people at Santa Fe were doing this in the early 90's but I have not
> > kept up with the literature. Where can I find an account of the state of
> > the art in this sort of modeling?
> >
>
> Try http://www.santafe.edu. Look on the home pages of Brian Arthur,
> Blake LeBaron, and William Brock.
>
The SFI market produced several papers, and its source code has been
open sourced. Pointers to these papers are on my web site listed
below. I have been working on a new artificial stock market which has
produced several working papers available on my web site.
I also have a working paper examing some of the power law like features
of financial data. One important issue is that many stochastic
processes can generate figures that look like power laws, so the finding
of a fractal looking picture may not tell you that much about what the
underlying process is.
In terms of agent based markets, many of these are capable of at least
generating "fat tailed" distributions for returns. (My website on agent
based computational finance contains some references to many different
agent based markets.)
Blake
- --
Blake LeBaron
Graduate School of International Economics and Finance
Brandeis University, Mailstop 032
Waltham, MA 02454-9110
http://www.brandeis.edu/~blebaron
781 736-2258
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--
John Conover, john@email.johncon.com, http://www.johncon.com/