This paper describes, analyzes and evaluates an algorithm for estimating portfolio loss probabilities using Monte Carlo simulation.Obtaining accurate estimates of such loss probabilities is essential to calculating value-at-risk, which is a quantile of the loss distribution. The method employs a...

This paper develops a variance reduction technique for Monte Carlo simulations of path-dependent options driven by high-dimensional Gaussian vectors. The method combines " importance sampling" based on a change of drift with "stratified sampling" along a small number of key dimensions. The...

This paper develops efficient methods for computing portfolio value-at-risk (VAR) when the underlying risk factors have a heavy-tailed distribution. In modeling heavy tails, we focus on multivariate "t" distributions and some extensions thereof. We develop two methods for VAR calculation that...

The special structure of regenerative processes is exploited to derive a new point estimate with very low bias for steady state quantities of regenerative simulations. If the simulation run length is t units of tune, the bias of the new estimate is of order 1/t² as opposed to the bias of order...

Infinitesimal Perturbation Analysis (IPA) is a method for computing a sample path derivative with respect to an input parameter in a discrete event simulation. The IPA algorithm is based on the fact that for certain parameters and any realization of a simulation, the change in parameter can be...

A simple and effective way to exploit parallel processors in discrete event simulations is to run multiple independent replications, in parallel, on multiple processors and to average the results at the end of the runs. We call this the method of parallel replications. This paper is concerned...

We modify the likelihood-based method for obtaining derivatives with respect to the rate of a Poisson process to that it is not necessary to know the exact value of that rate. This type of modification is necessary if the method is to be used on a sample path from a real system. The method is...

Consider a finite-state Markov chain where the transition probabilities differ by orders of magnitude. This Markov chain has an "attractor state," i.e., from any state of the Markov chain there exists a sample path of significant probability to the attractor state. There also exists a "rare...

This paper investigates the likelihood ratio method for estimating derivatives of finite-time performance measures in generalized semi-Markov processes (GSMPs). We develop readily verifiable conditions for the applicability of this method. Our conditions mainly place restrictions on the basic...