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...

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...

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...

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...

In this paper we investigate importance sampling techniques for the simulation of Markovian systems with highly reliable components. The need for simulation arises because the state space of such systems is typically huge, making numerical computation inefficient. Naive simulation is inefficient...

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...

Contingent capital in the form of debt that converts to equity when a bank faces financial distress has been proposed as a mechanism to enhance financial stability and avoid costly government rescues. Specific proposals vary in their choice of conversion trigger and conversion mechanism. We...

Monte Carlo simulation is widely used to measure the credit risk in portfolios of loans, corporate bonds, and other instruments subject to possible default. The accurate measurement of credit risk is often a rare-event simulation problem because default probabilities are low for highly rated...