Perpetuities with thin tails

We investigate the behaviour of P ( R ≧ r ) and P ( R ≦ − r ) as r → ∞for the random variable where is an independent, identically distributed sequence with P (− 1 ≦ M ≦ 1) = 1. Random variables of this type appear in insurance mathematics, as solutions of stochastic difference equations, in the analysis of probabilistic algorithms and elsewhere. Exponential and Poissonian tail behaviour can arise.