Improving the Asmussen-Kroese-Type Simulation Estimators

Abstract

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 X_1,...,X_N and N is a non-negative, integer-valued 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 non-negative. We also apply our ideas to estimate the quantity E[(S_N-u) ].

Keywords: Heavy-tailed random variables, efficient Monte Carlo simulation, Asmussen-Kroese estimators, stop-loss transform

JEL Classification: C15