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EazyE

Statistical Mechanics - ?

August 23rd, 2001, 7:22 pm

Ladies/Gents:I met a guy, Lester Ingber, recently who uses statistical mechanics to model asset pricing issues. He is the head quant at DRW Investments in Chicago - a very good options trading group.I am not familiar with this approach. He was a physics professor and said that it is used to model nonlinear diffusions and was originally developed for quantum physics.He has several papers describing them at his web site: www.ingber.comIs anyone familiar with these methods? Their pros and cons? How does one learn them? What is the incremental value from using nonlinear diffusions as opposed to linear processes?Thanks.
 
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Julian
Posts: 4
Joined: August 23rd, 2001, 12:19 pm

Statistical Mechanics - ?

August 28th, 2001, 9:23 am

Hi, EazyE.I am a physicist (I am finishing my Ph.D. in High Energy Physics) and I have recently become interested in this world of finance. Regarding your question I would say that I agree with the opinion of Paul in another thread: The more tools you have the better (the unique problem is to have enough time!). Moreover all tools are related, and the more easily you can switch from one to another the more insight you can have. Let me illustrate my point. You can start from a SDE and after doing and arbitrage free argument end with a PDE. In turn you can consider your PDE as an operator in a space of functions and use the tools of functional analysis. If you know something of quantum mechanics you know that there is and alternative way, invented by Feynman, to sove a PDE using path integrals. So you can write the solution of your PDE as a certain path integral. In some cases you can reduce this path integral to an ordinary integral and then you are done. Even if this is not possible there are several approximate methods in statistical physics to deal with non exactly solvable path integrals (like the saddle point approximation) that can give you approximate results good enough to save you a lot of computer time.Moreover, even though a given tool may not be the best suited for a certain situation it can give you a different perspective and a lot of intuition on the result.Julian