chill_factor said:
What type of techniques do you use in PDEs? Isn't finite-element just a method for solving PDEs?
There is a difference between "finite differencing methods" (FDM) and "finite element methods" (FEM). The wikipedia articles can go into details. FEM isn't very commonly used in finance. It's not clear to me whether this is because of some numerical reason or because of the people that get hired to crunch equations just come from an FDM background.
One other thing is that people in mathematical finance will make a distinction between "finite difference methods" and "finite volume methods" while people in my neck of computational astrophysics don't. Also, mathematical finance distinguishes between "tree" methods and "mesh" methods, but that's also a distinction that's not made in computational astrophysics, and that's clearly a "historical" distinction since they are mathematically equivalent. What happened was that two groups of people published the same techniques in different journals. The tree method came out of economics, whereas mesh methods come out of computational fluid dynamics.
Also this is a perfect example, of how I do use physics skills in my work. Boss person comes down and says we need to simulate that. I know the difference between FDM and FEM and so I come up with techniques to simulate it.
I've heard the term "financial engineering" used, but there is a very real sense in which what I do isn't engineering but rather physics. In engineering you are apply basic principles that do not change, and you aren't interested in figuring out what those principles are. A civil engineer applies Newtonian physics, but they don't have to worry about Newton's laws suddenly changing. If you have a situation where you don't know the basic principles, then an engineer is just going to go home.
However, in quantitative finance an "engineering" approach won't work, because the rules change, and often the goal is to figure out what the rules are. For example, since 2008, the rules involving interest rates have changed, and people haven't figured out what the exact equations for the new rules are. Figuring out fundamental and more or less universal principles from data is what defines "physics" in astronomy, and what defines an "astrophysicist."
One thing that I think is rather amusing is that when someone says that I'm not "doing physics" when they don't know what my job actually is. All you know is that I work in a bank and I sit in front of a computer all day, and that seems to be enough to define what I'm doing as "not physics." Suppose instead of modelling interest rates, I was modelling electron flows through semi-conductors. Well at that point I would be "doing physics", right? OK, so can you tell me the difference between the first and the second? Well I can't grab a handful of interest rates, but I also can't grab a handful of electrons, and I certainly can't grab a handful of neutrinos. Money is not "physical" but neither is gravity or time.
And what do you do if the editorial boards of Physica A and Physics Review E disagree with your definitions?
How much computational knowledge is necessary before it is actually useful? And how much computational knowledge should an experimental scientist know?
It depends on what you are trying to do. One good and bad thing about finance is that there are hundreds of different jobs with vastly different skills, and one odd thing is that every job is unique. It's not as if I have a fixed job title. It's very fluid, and one reason I like my work is that people do make an effort to fit my job to my skills, as well as to put some things that I'm bad at in the mix so that I learn new stuff.
One thing that is the case is that what I do doesn't work with an "industrial" model. You have a factory that produces standard widget part 43243 that fits into standard machine A34234. People tend to think the same way about degrees and jobs. You create major #34343 and that fits into career #B34234. Except that things don't work that way.
Also one thing that I do recommend that people do is to read lots of philosophy. What possible use is philosophy? Well we are in a discussion over names, and I've found that studying French post-structuralism and Marxist critical theory is pretty useful in thinking about how to make the system work for me. One thing that comes out of Marxist critical theory is that names are a political tool for the power holders in a society to maintain political and cultural hegemony. So if you want to change the definitions of words, you have to look at the politics and economics of a situation.
