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
Importance sampling for sums of random variables with regularly varying tails
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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For estimating P(Sn x) by simulation where Sk = Y1+...+Yk with Y1, ..., Yn are non-negative and heavy-tailed with distribution F, (Asmussen and Kroese 2006) suggested the estimator nF(Mn-1 ∨ (x -- Sn-1)) where Mk = max(Y1, ..., Yk). The estimator has shown to perform excellently in practice and has also nice theoretical properties. In particular, (Hartinger and Kortschak 2009) showed that the relative error goes to 0 as x → ∞. We identify here the exact rate of decay and propose some related estimators with even faster rates.