The Asmussen--Kroese Monte Carlo estimators of P(Sn > u) and P(SN > u) are known to work well in rare event settings, where SN is the sum of independent, identically distributed heavy-tailed random variables X1,...,XN and N is a nonnegative, integer-valued random variable independent of the Xi. In this paper we show how to improve the Asmussen--Kroese estimators of both probabilities when the Xi are nonnegative. We also apply our ideas to estimate the quantity E[(SN-u)+].
"Improving the Asmusse}--Kroese-type simulation estimators." J. Appl. Probab. 49 (4) 1188 - 1193, December 2012. https://doi.org/10.1239/jap/1354716666