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"... Perwez Shahabuddin was an accomplished researcher, teacher, and participant in the simulation community. This article provides an overview of his career and a summary of some of his many professional accomplishments. Categories and Subject Descriptors: A.0 [General Literature]: General—Biographies/a ..."
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Perwez Shahabuddin was an accomplished researcher, teacher, and participant in the simulation community. This article provides an overview of his career and a summary of some of his many professional accomplishments. Categories and Subject Descriptors: A.0 [General Literature]: General
and
"... Perwez Shahabuddin was an accomplished researcher, teacher, and participant in the simulation community. This article provides an overview of his career and a summary of some of his many professional accomplishments. Categories and Subject Descriptors: A.0 [General Literature]: General—Biographies/a ..."
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Perwez Shahabuddin was an accomplished researcher, teacher, and participant in the simulation community. This article provides an overview of his career and a summary of some of his many professional accomplishments. Categories and Subject Descriptors: A.0 [General Literature]: General
Scheduling Policies for an OnDemand Video Server with Batching
 in Proc. of ACM Multimedia
, 1994
"... In an ondemand video server environment, clients make requests for movies to a centralized video server. Due to the stringent response time requirements, continuous delivery of a video stream to the client has to be guaranteed by reserving sufficient resources required to deliver a stream. Hence th ..."
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Cited by 328 (8 self)
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In an ondemand video server environment, clients make requests for movies to a centralized video server. Due to the stringent response time requirements, continuous delivery of a video stream to the client has to be guaranteed by reserving sufficient resources required to deliver a stream. Hence there is a hard limit on the number of streams that can be simultaneously delivered by a server. The server can satisfy multiple requests for the same movie using a single disk I/O stream by sending the same data pages to multiple clients (using the multicast facility if present in the system). This can be achieved by batching requests for the same movie that arrive within a short duration of time. In this paper, we consider various policies for selecting the movie to be multicast. The choice of a policy depends very much on the customer waiting time tolerance before reneging. We show that an FCFS policy that schedules the movie with the longest outstanding request can perform better than the ...
FAST SIMULATION FOR MULTIFACTOR PORTFOLIO CREDIT RISK IN THE tCOPULA MODEL
, 2005
"... We present an importance sampling procedure for the estimation of multifactor portfolio credit risk for the tcopula model, i.e, the case where the risk factors have the multivariate t distribution. We use a version of the multivariate t that can be expressed as a ratio of a multivariate normal and ..."
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Cited by 21 (2 self)
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and a scaled chisquare random variable. The procedure consists of two steps. First, using the large deviations result for the Gaussian model in Glasserman, Kang, and Shahabuddin (2005a), we devise and apply a change of measure to the chisquare random variable. Then, conditional on the chi
Rare event simulation techniques for models of computer and communication systems
"... This talk reviews some of the fast simulation techniques used for estimating probabilities of rare events and related quantities in stochastic models of computer and communication systems. It is by no means a complete survey of these rare event simulation techniques. However, an attempt will be made ..."
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will be made to give some of the basic concepts, intuitions, and algorithms used for different types of stochastic models. The reader is referred to Heidelberger (1995) and Shahabuddin (1995) for recent comprehensive surveys in this area, and the reference list of Boots and Shahabuddin (2000) for some
Asymptotically Optimal Importance Sampling and Stratification for Pricing PathDependent Options
 Mathematical Finance
, 1999
"... This paper develops a variance reduction technique for Monte Carlo simulations of pathdependent options driven by highdimensional Gaussian vectors. The method combines importance sampling based on a change of drift with stratified sampling along a small number of key dimensions. The change of dri ..."
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Cited by 90 (13 self)
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This paper develops a variance reduction technique for Monte Carlo simulations of pathdependent options driven by highdimensional Gaussian vectors. The method combines importance sampling based on a change of drift with stratified sampling along a small number of key dimensions. The change of drift is selected through a large deviations analysis and is shown to be optimal in an asymptotic sense. The drift selected has an interpretation as the path of the underlying state variables which maximizes the product of probability and payoffthe most important path. The directions used for stratified sampling are optimal for a quadratic approximation to the integrand or payoff function. Indeed, under differentiability assumptions our importance sampling method eliminates variability due to the linear part of the payoff function, and stratification eliminates much of the variability due to the quadratic part of the payoff. The two parts of the method are linked because the asymptotically optimal drift vector frequently provides a particularly effective direction for stratification. We illustrate the use of the method with pathdependent options, a stochastic volatility model, and interest rate derivatives. The method reveals novel features of the structure of their payoffs. KEY WORDS: Monte Carlo methods, variance reduction, large deviations, Laplace principle 1. INTRODUCTION This paper develops a variance reduction technique for Monte Carlo simulations driven by highdimensional Gaussian vectors, with particular emphasis on the pricing of pathdependent options. The method combines importance sampling based on a change of drift with stratified sampling along a small number of key dimensions. The change of drift is selected through a large deviations analysis and is shown to...
Multilevel Splitting for Estimating Rare Event Probabilities
 OPERATIONS RESEARCH
, 1999
"... The estimation of rare event probabilities poses some of the of the most difficult computational challenges for Monte Carlo simulation and, at the same time, some of the greatest opportunities for efficiency improvement through the use of variance reduction techniques. Current interest in rare event ..."
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Cited by 75 (4 self)
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The estimation of rare event probabilities poses some of the of the most difficult computational challenges for Monte Carlo simulation and, at the same time, some of the greatest opportunities for efficiency improvement through the use of variance reduction techniques. Current interest in rare events stems primarily from developments in computer and communications technology: many industrial and scientific applications require highly reliable computer systems (with correspondingly small failure probabilities), and standards for emerging telecommunications systems call for extremely small bufferoverflow probabilities. The performance of these types of systems is frequently studied through simulation, but straightforward simulation can easily produce estimates that are off by orders of magnitude in estimating small probabilities. In these settings, variance reduction is essential. Importance sampling, based on changing probability distributions to make rare events less rare, has been used to obtain dramatic improvements in efficiency in estimating small probabilities in queueing and reliability systems (see [4] and [7] for overviews). But the effectiveness of importance sampling depends critically on the ability to find the right change of measure; indeed, used improperly importance sampling is liable to produce worse results than straightforward simulation. Finding the right change of measure generally requires identifying at least the rough asymptotics of a rare event probability, often described by a large deviations result. This type of analysis can be formidable in complex models, so the domain of importance sampling, while substantial, does not include all problems of interest. This work deals with an alternative method for rare event simulation that uses the technique of splitting
Portfolio ValueatRisk with HeavyTailed Risk Factors,” Mathematical Finance 12
, 2002
"... This paper develops efficient methods for computing portfolio valueatrisk (VAR) when the underlying risk factors have a heavytailed distribution. In modeling heavy tails, we focus on multivariate t distributions and some extensions thereof. We develop two methods for VAR calculation that exploit ..."
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Cited by 63 (2 self)
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This paper develops efficient methods for computing portfolio valueatrisk (VAR) when the underlying risk factors have a heavytailed distribution. In modeling heavy tails, we focus on multivariate t distributions and some extensions thereof. We develop two methods for VAR calculation that exploit a quadratic approximation to the portfolio loss, such as the deltagamma approximation. In the first method, we derive the characteristic function of the quadratic approximation and then use numerical transform inversion to approximate the portfolio loss distribution. Because the quadratic approximation may not always yield accurate VAR estimates, we also develop a low variance Monte Carlo method. This method uses the quadratic approximation to guide the selection of an effective importance sampling distribution that samples risk factors so that large losses occur more often. Variance is further reduced by combining the importance sampling with stratified sampling. Numerical results on a variety of test portfolios indicate that large variance reductions are typically obtained. Both methods developed in this paper overcome difficulties associated with VAR calculation with heavytailed risk factors. The Monte Carlo method also extends to the problem of estimating the conditional excess, sometimes known as the conditional VAR.
Effective Bandwidth and Fast Simulation of ATM Intree Networks
, 1992
"... We consider the efficient estimation, via simulation, of very low buffer overflow probabilities in certain acyclic ATM queueing networks. We apply the theory of effective bandwidths and Markov additive processes to derive an asymptotically optimal simulation scheme for estimating such probabilities ..."
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Cited by 63 (14 self)
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We consider the efficient estimation, via simulation, of very low buffer overflow probabilities in certain acyclic ATM queueing networks. We apply the theory of effective bandwidths and Markov additive processes to derive an asymptotically optimal simulation scheme for estimating such probabilities for a single queue with multiple independent sources, each of which may be either a Markov modulated process or an autoregressive processes. This result extends earlier work on queues with either independent arrivals or with a single Markov modulated arrival source. The results are then extended to estimating loss probabilities for intree networks of such queues. Experimental results show that the method can provide many orders of magnitude reduction in variance in complex queueing systems that are not amenable to analysis.
P.: Quick simulation methods for estimating the unreliability of regenerative models of large highly reliable systems
 Probability in the Engineering and Information Sciences
, 2004
"... We investigate fast simulation techniques for estimating the unreliability in large Markovian models of highly reliable systems for which analytical0numerical techniques are difficult to apply+ We first show mathematically that for “small ” time horizons, the relative simulation error, when using th ..."
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Cited by 4 (0 self)
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+ These techniques extend to nonMarkovian, highly reliable systems as long as the regenerative structure is preserved+ © 2004 Cambridge University Press 02699648004 $16+00 339340 M. K. Nakayama and P. Shahabuddin 1.
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