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...

For {Xi}i = 1 a sequence of i.i.d. random variables taking values in a Polish space [Sigma] with distribution [mu], we obtain large and moderate deviation principles for the processes {n-1 [Sigma][nt]i = 1 [delta]Xi; t = 0}n = 1 and {n-1/2 [Sigma][nt]i = 1 ([delta]Xi - [mu]); t = 0}n = 1,...

The large deviation principle is known to hold for the empirical measures (occupation times) of Polish space valued random variables and for the empirical means of Banach space valued random variables under Markov dependence or mixing conditions, and subject to the appropriate exponential tail...

The large deviation principle is shown to hold for a class of stochastic recursive algorithms based on a sequence of random variables satisfying an appropriate mixing condition.

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...

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...