We show how, from a single simulation run, to estimate the ruin probabilities and their sensitivities (derivatives) in a classic insurance risk model under various distributions of the number of claims and the claim size. Similar analysis is given for the tail probabilities of the accumulated...

Some theoretical and practical aspects antithetic and common random numbers for variance reduction in simulation of stochastic systems with dependent elements are considered. A proof of their optimality in estimating the expected value of the response sum or the response difference of a pair of...

In this paper we show how an optimization problem involving the expected performance of a stochastic system can be estimated using a single simulation experiment. The proposed method is based on a probability measure transformation and generation of a stochastic counterpart to the deterministic...

We define modified importance sampling and discuss conditions under which variance reduction is possible relative to the Crude Monte Carlo method. Application of modified importance sampling to the “what if” problem and to sensitivity analysis of discrete-event systems are given. Numerical...

Some theoretical and practical aspect of the score function (SF) approach for estimating the sensitivities of computer simulation models and solving the so-called “what if” problem (performance extrapolation) are considered. It is shown that both the sensitivities (gradients, Hessians, etc.)...

We provide a generalization of Hoeffding's inequality to partial sums that are derived from a uniformly ergodic Markov chain. Our exponential inequality on the deviation of these sums from their expectation is particularly useful in situations where we require uniform control on the constants...

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...