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The Danger of Modeling Complex Systems

This is an excellent article from a few weeks ago that describes one of the proximate causes of the current financial crisis.

For five years, Li’s formula, known as a Gaussian copula function, looked like an unambiguously positive breakthrough, a piece of financial technology that allowed hugely complex risks to be modeled with more ease and accuracy than ever before. With his brilliant spark of mathematical legerdemain, Li made it possible for traders to sell vast quantities of new securities, expanding financial markets to unimaginable levels.

Read the whole thing.  I am by no means a mathematician, but I work for a company that does mathematical modeling of a complex system (ligands binding to proteins), so I have some experience with the benefits and deficiencies of such systems, as well as some experience with what happens when the uninitiated try to understand these models.  Let’s just say there’s a strong tendency to celebrate the benefits and fail to appreciate the limitations.

I think there’s a lot of this when it comes to global warming, too, which is another complex system that people have attempted to model.  It’s always a good idea that when anyone claims to have a mathematical model of a complex system that is simply revolutionary, without any significant limitation of caveat, drag him into the nearest bathroom and beat him senseless, before he destroys civilization as we know it.  Entire industries have been ruined by such people, who are seldom the people who actually developed the models, and understand the limitations.  Finance is not the only industry, just the latest.

2 Responses to “The Danger of Modeling Complex Systems”

  1. Jdude says:

    Math is hard.

    -Barbie
    -Early Pentium processors

    The next time someone tires to baffle me with bullmath, I’ll happily beat them about the head.

    “Let’s just say there’s a strong tendency to celebrate the benefits and fail to appreciate the limitations.”

    I think this is a human trait, which may be why people are scammed so often. Aside from mind numbing boring research, is there a general rule that one can use to look for the traps? Something catchy like “If the math is too hard, hide your credit card” or “If it makes no sense, keep your cents”? ;)

    -Jdude

  2. While this was certainly part of the complex failure, there’s an even more obvious part of the failure, and it was recognized when the policy changed. At http://www.claytoncramer.com/weblog/2009_03_01_archive.html#2347803771083807218 I link to a September 30, 1999 New York Times article about the change in policy to encourage subprime mortgage lending–and one expert warned that it would lead to a massive bailout by the federal government if the economy ever turned down. Also, a link to a September 11, 2003 New York Times article about Bush Administration efforts to regulate subprime mortgage lending, and Democratic efforts to stop it.

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