**** you, method of characteristics

[KrazyHorse]

Plan for the next 2.25 days:

1) PDEs:
a) Classical analytic methods, esp. as applied to heat equation. Free boundary conditions. Fundamental solutions. Tie in with BSM PDE.
b) Numerical methods, esp. FD (crank-nicholson and upwind differencing)

2) Numerical matrix algebra (LU decomp, SVD, Cholesky decomp)

3) Stochastic processes, Ito calculus, Kolmogorov equation/Feynman-Kac formula. Application to BM and GBM

4) Monte Carlo methods. RNGs, importance sampling, antithetic variables, other variance reduction methods(?). Tie-in with Radon-Nikodym deriv. and Girsanov. Skim original paper on VEGAS. Markov chains (Gibbs sampling, Metropolis-Hastings algorithm). Current state of research on MC methods in options pricing.

5) Statistical methods. PCA, GARCH, EWMV etc.

6) Finance crap. Skim through Hull for definitions/conventions. CAPM, interest rate derivatives, yadda yadda.

7) C++. Skim Eckel for key points.

[KrazyHorse]

chances are 50%, knowing his background, that he asks me to solve heat equation on a cylinder.

[Asher]

I do that every morning while making my coffee.

[KrazyHorse]

Either that was extremely clever, or you got very lucky.

[Japher]

Ah, young Grashoffer... take the cylinder from my hand and enter the evil empire you will.

(seriously, heat transfer needs more puns..)

[Felch]

Death to all Goldman Sachs employees!

Is this some new meme that I missed out on?

[Guynemer]

I do that every morning while making my coffee.

Either that was extremely clever, or you got very lucky.

[SpencerH]

So Goldman Sachs is looking to hire a physicist who is boning up on his math in case he gets asked about "heat equation on a cylinder"! Something smells fishy here, where are these financial types located, area 51?

[KrazyHorse]

Solving a heat eq. on cyl. = easy. The hard part comes when he starts throwing in curveballs.

BTW, the process is as follows:

Stock/commodity/interest rates/etc. prices are random -> They follow brownian motion -> They obey the diffusion/heat equation (sort of) -> All other claims BASED on those prices also obey some version of the heat equation, or can be made to look like they do if you squint hard enough -> The solution to the heat equation in a cylinder is bessel functions -> This guy did research on numerical methods involving bessel functions -> He will ask me to solve the heat eqn on a cylinder

[KrazyHorse]

Why can't KH use his knowledge for good, instead of evil?

The economy doesn't plan itself. A commie should know that.

[chequita guevara]

He could use his knowledge to help solve the mysteries of the universe. Instead, he's going to help the capitalists rape America.

[KrazyHorse]

I'm going to do far more social good in finance than in a physics department.

[Ramo]

Solving a heat eq. on cyl. = easy. The hard part comes when he starts throwing in curveballs.

BTW, the process is as follows:

Stock/commodity/interest rates/etc. prices are random -> They follow brownian motion -> They obey the diffusion/heat equation (sort of) -> All other claims BASED on those prices also obey some version of the heat equation, or can be made to look like they do if you squint hard enough -> The solution to the heat equation in a cylinder is bessel functions -> This guy did research on numerical methods involving bessel functions -> He will ask me to solve the heat eqn on a cylinder

That's what he wants you to think. Bone up on spherical harmonics too.

[KrazyHorse]

Spherical harmonics are fine. I will Wigner 3j symbol his ass.

[KrazyHorse]

I wrote a gaussian smoothing kernel in a basis of Ylm about 3-4 years ago. It was awesome. Then I found out that everybody just uses flat space kernels.