Abstract: A computer implemented method prices derivative securities (for example, options) by selecting an importance sampling (IS) distribution and combining the chosen IS distribution with stratified sampling. The process consists of the steps of choosing an importance sampling distribution and combining the chosen importance sampling with stratification or Quasi-Monte Carlo (QMC) simulation. In the first step, an importance sampling distribution is chosen. In the second step, the chosen importance sampling is combined with stratification or Quasi-Monte Carlo sequencing. The pricing of many types of securities reduces to one of estimating an expectation of a real-valued function of some random variables.

Abstract: An integrated scheduling approach that provides VCR control functions to clients without always requiring a separate video stream for all clients. When a client invokes a resume, following a pause, the system uses a hierarchy of methods to handle the request. If an ongoing video stream is available such that the point at which the client is paused will be reached by that stream within a tolerable delay, the client is assigned to the ongoing stream. If no such stream is available, and the client request can not be served from a buffer, the system assigns the client to a reserve stream taken from a pool of reserved server capacity. If no reserved server capacity is available, the client is given priority for assignment to the next stream to become available.