Finance Theory

In the couple of economics courses that I have taken, I have generally best understood the material that was presented to me in a very mathematical way. I was pretty good at understanding all the graphs, and very mediocre at comprehending the material when it was described in long paragraphs. That's probably because I'm disposed to think fairly mathematically, because I'm a visual person, and because I'm pretty decent at connecting the two. The problem, however, is that (I think) many people (perhaps the majority) in the classes that I have taken, are the opposite, and that the economic models we learn at this level are so simple that writing the mathematical formalisms for them is a little silly when a bit of prose will do. Naturally though, I have this desire to turn it all into mathematics, because it's easier for me to understand it that way.

As we all know, the summer is approaching, and I am becoming profoundly unmotivated to work on school-relating projects. Even though my mother is away from home this weekend at my sister's graduation, and no one is home but me, I still get distracted absurdly easily nowadays when I try to work. In response to this, I now walk over to the library at Lewis and Clark and do most of my homework there, so that I can actually get a little accomplished. As you might imagine, I still get distracted there fairly easily because, well, there are hundreds of thousands of books everywhere, and some of them are bound to be pretty interesting. In response to my feelings on maths and economics, I have been taking breaks from writing by browsing the stacks on these subjects. In the process, I have come across the fascinating subject of finance theory. It's essentially the theory of how equity markets function, which is interesting to me because of my peripheral interest in the stock market. Today, I checked out an introduction to this so-called "financial engineering," and it really is fantastic stuff. Instead of being full of graphs and multiple regressions, the book is filled with of theorems and proofs. And it's fairly approachable material too. It seems that one can squeak by (at least in the book I got) with multivariate calculus, and just the tinist bit of differential equations and linear algebra (mostly just at the level of manipulating matrices).

It gets even better though: We all know that physicists are fairly bright people, and also that they're a tad arrogant. So, of course, physicists have marched into the field of finance theory brandishing a bunch of weapons from statistical mechanics, using them to attack the problem of how markets behave. They call this interdisciplinary field "econophysics." There are supposedly lots of problems with much of conventional finance theory, especially in the assumptions it makes. The assumption of rational expectations, for example, can apparently become slightly problematic when you consider that the stock market is replete with irrational exuberance every day. From what I gather, the main premise of econophysics is that financial markets are essentially chaotic systems that don't reach equilibria like conventional theory predicts. Instead, they use things like Brownian motion, Lévy somethingorothers, and various other devices from statistical mechanics to model these financial phenomena. Maybe it's a bit of a stretch to say that investors behave like gas bubbles, but it's very intriguing nonetheless.