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 GI/GI/1 queues and insurance risk processes with subexponential distributions
Proceedings of the 32nd conference on Winter simulation
Simulating heavy tailed processes using delayed hazard rate twisting
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Efficient simulation for large deviation probabilities of sums of heavy-tailed increments
Proceedings of the 38th conference on Winter simulation
Importance sampling for sums of random variables with regularly varying 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
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We consider importance sampling simulation for estimating rare event probabilities in the presence of heavy-tailed distributions that have polynomial-like tails. In particular, we prove the following negative result: there does not exist an asymptotically optimal state-independent change-of-measure for estimating the probability that a random walk (respectively, queue length for a single server queue) exceeds a "high" threshold before going below zero (respectively, becoming empty). Furthermore, we derive explicit bounds on the best asymptotic variance reduction achieved by importance sampling relative to naïve simulation. We illustrate through a simple numerical example that a "good" state-dependent change-of-measure may be developed based on an approximation of the zero-variance measure.