Perpetuities with thin tails revisited

Perpetuities with Thin Tails

Fat Tails, Thin Tails, and Climate Change Policy

How much environmental damage would result from unabated water pollution, greenhouse gas (GHG) emissions, toxic waste disposal, and other potentially destructive activities? And whatever that environmental damage is expected to be, what economic and social cost will it have? In other words, what is the benefit of taking costly actions today or in the near future to reduce rates of pollution and...

Simulating Perpetuities

A perpetuity is a random variable that can be represented as 1 + W 1 + W 1 W 2 + W 1 W 2 W 3 + , where the W i 's are i.i.d. random variables. We study exact random variate generation for perpetuities and discuss the expected complexity. For the Vervaat family, in which W 1 L = U 1== , > 0, U uniform 0; 1], all the details of a novel rejection method are worked out. There exists an implementati...

Appendix to “Approximating perpetuities”

An algorithm for perfect simulation from the unique solution of the distributional fixed point equation Y =d UY +U(1−U) is constructed, where Y and U are independent and U is uniformly distributed on [0, 1]. This distribution comes up as a limit distribution in the probabilistic analysis of the Quickselect algorithm. Our simulation algorithm is based on coupling from the past with a multigamma ...

Stability of Perpetuities

For a series of randomly discounted terms we give an integral criterion to distinguish between almost-sure absolute convergence and divergence in probability to 1, these being the only possible forms of asymptotic behaviour. This solves the existence problem for a one-dimensional perpetuity that remains from a 1979 study by Vervaat, and yields a complete characterization of the existence of dis...