Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Simulating heavy tailed processes using delayed hazard rate twisting
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 rare event simulation for heavy-tailed compound sums
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
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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State-dependent importance sampling algorithms based on mixtures are considered. The algorithms are designed to compute tail probabilities of a heavy-tailed random walk. The increments of the random walk are assumed to have a regularly varying distribution. Sufficient conditions for obtaining bounded relative error are presented for rather general mixture algorithms. Two new examples, called the generalized Pareto mixture and the scaling mixture, are introduced. Both examples have good asymptotic properties and, in contrast to some of the existing algorithms, they are very easy to implement. Their performance is illustrated by numerical experiments. Finally, it is proved that mixture algorithms of this kind can be designed to have vanishing relative error.