Perpetuities with thin tails

Charles M. Goldie · Rudolf Grübel

104 citations0/0 files storedAdvances in Applied Probability

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Probability and Risk Models Probability and Statistical Research Stochastic processes and statistical mechanics

Abstract

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.

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1977On the infinite divisibility of the lognormal distribution

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2005Large deviations and ruin probabilities for solutions to stochastic recurrence equations with heavy-tailed innovations 2009Extreme Value Theory for GARCH Processes 2007On a Theorem of Breiman and a Class of Random Difference Equations 2016A note on the Kesten–Grincevičius–Goldie theorem 2018Bernstein-gamma functions and exponential functionals of Lévy processes

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