The Asmussen-Kroese Monte Carlo estimators of P(S n > u) and P(S N > u) are known to work well in rare event settings, where S n is the sum of independent, identically distributed heavy-tailed random variables X₁, ..., X n and N is a nonnegative, integervalued random variable independent of the X i . In this paper we show how to improve the Asmussen-Kroese estimators of both probabilities when the X i are nonnegative. We also apply our ideas to estimate the quantity E[(S N – u)⁺].
December 1, 2012
Journal of Applied Probability, 49 (4), 2012.