Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Proceedings of the 33nd conference on Winter simulation
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)
A large deviations view of asymptotic efficiency for simulation estimators
Proceedings of the 40th Conference on Winter Simulation
Introduction to Rare Event Simulation
Introduction to Rare Event Simulation
On the inefficiency of state-independent importance sampling in the presence of heavy tails
Operations Research Letters
On importance sampling with mixtures for random walks with heavy tails
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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We develop an efficient importance sampling algorithm for estimating the tail distribution of heavy-tailed compound sums, that is, random variables of the form SM=Z1+&cdots;+ZM where the Zi's are independently and identically distributed (i.i.d.) random variables in R and M is a nonnegative, integer-valued random variable independent of the Zi's. We construct the first estimator that can be rigorously shown to be strongly efficient only under the assumption that the Zi's are subexponential and M is light-tailed. Our estimator is based on state-dependent importance sampling and we use Lyapunov-type inequalities to control its second moment. The performance of our estimator is empirically illustrated in various instances involving popular heavy-tailed models.