The web is an extremely dynamic world where information is updated even every second. A web information monitoring system fetches information from the web continuously and finds changes by compar- ing two versions of the same page. The updating of a specific web page is modeled as a Poisson process with parameter to indicate the change frequency. As the amount of computing resources is limited, it is nec- essary to find some policies for reducing the overall change-detection time. Different allocation schemas are evaluated experimentally to find out which one is the most suitable for the web information monitoring prob- lem. The experimental data shows the runtime characteristics of the overall system performance and the re- lationship to the total amount of resources.
Mathematically, the Black-Scholes model of American option pricing is a free boundary problem of partial differential equation. It is well known that this model is a nonlinear problem, and it has no closed form solution. We can only obtain an approximate solution by numerical method, but the precision and stability are hard to control, because the singularity at the exercise boundary near expiration date has a great effect on precision and stability for numerical method. We propose a new numerical method, FDA method, to solve the American option pricing problem, which combines advantages the Semi-Analytical Method and the Front-Fixed Difference Method. Using the FDA method overcomes the difficulty resulting from the singularity at the terminal of optimal exercise boundary. A large amount of calculation shows that the FDA method is more accurate and stable than other numerical methods.
