New efficient estimators in rare event simulation with heavy tails

This paper is concerned with the efficient simulation of P (Sn > s) where Sn is the sum of n i.i.d. heavy-tailed random variables X1, . . . ,Xn. Asmussen and Kroese (2006) and Asmussen and Kortschak (2012) proposed estimators that combine exchangeability arguments with conditional Monte-Carlo and whose relative errors go to 0 as s→∞. We useMn = max (X1, . . . ,Xn) as a control variate to propose new efficient estimators with smaller relative errors and give upper bounds of their rates of decay.