Importance sampling for stochastic simulations
Management Science
Fast simulation of rare events in queueing and reliability models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Simulating heavy tailed processes using delayed hazard rate twisting
Proceedings of the 31st conference on Winter simulation: Simulation---a bridge to the future - Volume 1
ACM SIGMETRICS Performance Evaluation Review
The Transform Likelihood Ratio Method for Rare Event Simulation with Heavy Tails
Queueing Systems: Theory and Applications
Proceedings of the 35th conference on Winter simulation: driving innovation
A unified approach for finite-dimensional, rare-event Monte Carlo simulation
WSC '04 Proceedings of the 36th conference on Winter simulation
Importance sampling simulation in the presence of heavy tails
WSC '05 Proceedings of the 37th conference on Winter simulation
Efficient simulation for large deviation probabilities of sums of heavy-tailed increments
Proceedings of the 38th conference on Winter simulation
Perwez Shahabuddin, 1962--2005: A professional appreciation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Asymptotics and fast simulation for tail probabilities of maximum of sums of few random variables
ACM Transactions on Modeling and Computer Simulation (TOMACS)
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Importance sampling for sums of random variables with regularly varying tails
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Efficient tail estimation for sums of correlated lognormals
Proceedings of the 40th Conference on Winter Simulation
Efficient rare event simulation for heavy-tailed compound sums
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On importance sampling with mixtures for random walks with heavy tails
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On the inefficiency of state-independent importance sampling in the presence of heavy tails
Operations Research Letters
Improved cross-entropy method for estimation
Statistics and Computing
Rare event simulation techniques
Proceedings of the Winter Simulation Conference
Rare-event simulation for stochastic recurrence equations with heavy-tailed innovations
ACM Transactions on Modeling and Computer Simulation (TOMACS)
New efficient estimators in rare event simulation with heavy tails
Journal of Computational and Applied Mathematics
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Consider the problem of estimating the small probability that the maximum of a random walk exceeds a large threshold, when the process has a negative drift and the underlying random variables may have heavy tailed distributions, that is, their tail distribution decays at a subexponential rate. We consider one class of such problems that has applications in estimating the ruin probability associated with insurance claim processes with subexponentially distributed claim sizes, and in estimating the probability of large delays in an M/G/1 queue with subexponentially distributed service times. Significant work has been done on analogous problems for the light tailed case (when the tail distribution decreases at an exponential rate or faster) that involve importance sampling methods using appropriate exponential twisting. However, for the subexponential case, such exponential twisting is infeasible and alternative techniques are needed. In this paper we introduce importance sampling techniques where the new probability measure is obtained by twisting the hazard rate of the original distribution. For subexponential distributions this amounts to subexponential twisting---twisting at a subexponential rate. In addition, we introduce the technique of "delaying" the twisting and show that the combination of the two techniques produces asymptotically optimal estimates of the small probability mentioned above.