Asian options paying the excess over strike, of either the arithmetic or geometric average of the asset price over either discrete or continuous time, are valued using analytical and simulation methodologies. Expressions are developed for the double Laplace transform of the continuous arithmetic Asian option in both its strike and maturity. Analytical option prices for the continuous arithmetic...

We propose an approximate static hedging procedure for multivariate derivatives. The hedging portfolio is composed of statically held simple univariate options, optimally weighted minimizing the variance of the difference between the target claim and the approximate replicating portfolio. The method uses simulated paths to estimate the weights of the hedging portfolio and is related to Monte Ca...

Simulation-based wafer fabrication optimization models require extensive computational time to obtain accurate estimates of output parameters. This research seeks to develop goal-driven optimization methodologies for a variety of semiconductor manufacturing problems using appropriate combinations of “resource-driven” (R-D), “job-driven” (J-D), and Mixed (combination of R-D and J-D) models to re...

We present the Optimizing Control Variate (OCV) estimator, a new estimator for Monte Carlo rendering. Based upon a deterministic sampling framework, OCV allows multiple importance sampling functions to be combined in one algorithm. Its optimizing nature addresses a major problem with control variate estimators for rendering: users supply a generic correlated function which is optimized for each...

The canonical variates can be calculated from the eigenvectors of the within-group sums of squares and cross-products matrix. However, G03ACF calculates the canonical variates by means of a singular value decomposition (SVD) of a matrix V . Let the data matrix with variable (column) means subtracted be X and let its rank be k; then the k by (ng 1) matrix V is given by: V 1⁄4 QXQg; where Qg is a...

– For any problem that asks you to provide an algorithm, be sure to give a step-by-step algorithm. Do not explain how to implement your algorithm in Arena or Excel, but rather, you should provide an algorithm (i.e., pseudo-code) that can be implemented in any language. Also, for any random variates needed by your algorithm, be sure to explicitly provide the steps needed to generate the random v...

Pseudo-random numbers – both uniform and non-uniform – are used in random sampling, simulation, and Monte-Carlo estimation. Base SAS software contains numerous random number, quantile, and probability functions allowing the user to generate a selection of nominal, discrete, and continuous random variates. Other variates may be generated with a data step, often making use of SAS functions. We wi...

We present a computationally efficient method to generate random variables from a univariate conditional probability density function (PDF) derived from a multivariate α-sub-Gaussian (αSG) distribution. The approach may be used to sequentially generate variates for sliding-window models that constrain immediately adjacent samples to be αSG random vectors. We initially derive and establish vario...

We suggest a new class of metrics for measuring distances between documents, generalizing the well-known resemblance distance. We then show how to combine distance measures with statistical smoothing to develop techniques for imputing missing features of documents. We treat in detail the case where these features are continuous variates, but we note that our methods can be adapted to settings w...

There has been a great interest in the use of variance reduction techniques VRTs in simulation output analysis for the purpose of improving accuracy when the performance measurements of complex production and service systems are estimated. Therefore, a simulation output analysis to improve the accuracy and reliability of the output is required. The performance measurements are required to have ...