Decision, Operations & Information Technologies

Permanent URI for this communityhttp://hdl.handle.net/1903/2230

Prior to January 4, 2009, this unit was named Decision & Information Technologies.

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Subject: search.filters.subject.simulation

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Now showing 1 - 4 of 4
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    A Large Deviations Analysis of Quantile Estimation with Application to Value at Risk
    (2005-07-01T12:31:49Z) Jin, Xing; Fu, Michael C.
    Quantile estimation has become increasingly important, particularly in the financial industry, where Value-at-Risk has emerged as a standard measurement tool for controlling portfolio risk. In this paper we apply the theory of large deviations to analyze various simulation-based quantile estimators. First, we show that the coverage probability of the standard quantile estimator converges to one exponentially fast with sample size. Then we introduce a new quantile estimator that has a provably faster convergence rate. Furthermore, we show that the coverage probability for this new estimator can be guaranteed to be 100% with sufficiently large, but finite, sample size. Numerical experiments on a VaR example illustrate the potential for dramatic variance reduction.
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    Sensitivity Analysis for Monte Carlo Simulation of Option Pricing
    (1995) Fu, Michael C.; Hu, Jian-Qiang
    Monte Carlo simulation is one alternative for analyzing options markets when the assumptions of simpler analytical models are violated. We introduce techniques for the sensitivity analysis of option pricing which can be efficiently carried out in the simulation. In particular, using these techniques, a single run of the simulation would often provide not only an estimate of the option value but also estimates of the sensitivities of the option value to various parameters of the model. Both European and American options are considered, starting with simple analytically tractable models to present the idea and proceeding to more complicated examples. We then propose an approach for the pricing of options with early exercise features by incorporating the gradient estimates in an iterative stochastic approximation algorithm. The procedure is illustrated in a simple example estimating the option value of an American call. Numerical results indicate that the additional computational effort required over that required to estimate a European option is relatively small.
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    Stochastic Gradient Estimation
    (2005-07-01T12:31:02Z) Fu, Michael C.
    We consider the problem of efficiently estimating gradients from stochastic simulation. Although the primary motivation is their use in simulation optimization, the resulting estimators can also be useful in other ways, e.g., sensitivity analysis. The main approaches described are finite differences (including simultaneous perturbations), perturbation analysis, the likelihood ratio/score function method, and the use of weak derivatives.
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    EVALUATION OF SETUP ECONOMIES IN CELLULAR MANUFACTURING
    (2004-08-04) Kramer, Steven; Assad, Arjang A; Decision and Information Technologies; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    This dissertation addresses two research questions relating to the role of setups in discrete parts manufacturing. The first research topic uses a carefully designed simulation study to investigate the role of setup economies in the factory-wide conversion of functional layouts (job shops) to cellular manufacturing. The model-based literature shows a wide dispersion in the relative performance of cellular manufacturing systems as compared to the original job-shop configurations, even when the key performance measure is flow time and the assessment tool used is simulation. Using a standardized framework for comparison, we show how this dispersion can be reduced and consistent results can be obtained as to when the conversion of the job shop is advantageous. The proposed framework standardizes the parameters and operational rules to permit meaningful comparison across different manufacturing environments, while retaining differences in part mix and demand characteristics. We apply this framework to a test bed of six problems extracted from the literature and use the results to assess the effect of two key factors: setup reduction and the overall shop load (demand placed on the available capacity). We also show that the use of transfer batches constitutes an independent improvement lever for reducing flow time across all data sets. Finally, we utilize the same simulation study framework to investigate the benefits of partial transformation, where only a portion of the job shop is converted to cells to work alongside a remainder shop. The second research question examines the role of dispatching rules in the reduction of setups. We use queueing models to investigate the extent of setup reduction analytically. We single out the Alternating Priority (AP) rule since it is designed to minimize the incidence of setups for a two-class system. We investigate the extent of setup reductions by comparing AP with the First-Come-First-Served (FCFS) rule. New results are obtained analytically for the case of zero setup times and extended to the case of non-zero setup time through computational studies.