Improving the Asmussen – Kroese Type Simulation Estimators

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)⁺].

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