Papers

These are 2 very modest papers that I wrote as memos for myself.

Black-Scholes PDE derivation and solution paper is a compilation of intricate mathematical details that I gathered from several sources. Unfortunately financial engineering books mostly omit mathimatical beauty of the approach to the solution of this equation. Indeed Myron Scholes said that it took them only 6 month to derive this equation and another 3 years to solve it.

Another paper were inspired by my interest in learning inner workings of RSA algorithm. I found a very helpful RSA primer at http://fringe.davesource.com/Fringe/Crypt/RSA/Algorithm.html and then started looking at fast primality test algorithms. I wanted to implement Miller-Rabin primality test in CUDA C (this will be a separate topic). Looking at existing OpenSSH implementation I found that candidates were initially pre-tested by simple division by small primes. I immediately realized that number of small primes used for pre-test is actually a function of prime number candidate length. I derived simple and elegant solution approach to this problem which you can find in Miller-Rabin optimization paper.