On the Laplace transform of perpetuities with thin tails
Abstract
We consider the random variables R which are solutions of the distributional equation R=MR+Q, where (Q,M) is independent of R and M≤ 1. Goldie and Gr\"ubel showed that the tails of R are no heavier than exponential. In this note we provide the exact lower and upper bounds of the domain of the Laplace transform of R.
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