Appendix to “Approximating perpetuities”

An interesting family of Black-Scholes perpetuities

We obtain the Laplace transform and integrability properties of the integral over R+ of the call quantity associated with geometric Brownian motion with negative drift, thus adding a new element to the list of already studied Brownian perpetuities.

Perfect simulation of Vervaat perpetuities

We use coupling into and from the past to sample perfectly in a simple and provably fast fashion from the Vervaat family of perpetuities. The family includes the Dickman distribution, which arises both in number theory and in the analysis of the Quickselect algorithm (the motivation for our work).

Stabilität von Perpetuities

Gametes, embryos and the life in being: the impact of reproductive technology on the rule against perpetuities.

As the twenty-first century begins, changing technology is testing old rules of property law. In this Article, the author discusses the effect of modern technology on the Role Against Perpetuities. This discussion includes the arguments for and against recognition of the embryo as a life in being, as well as suggestions for legislative solutions to this issue.

On distributional properties of perpetuities

We study probability distributions of convergent random series of a special structure, called perpetuities. By giving a new argument, we prove that such distributions are of pure type: degenerate, absolutely continuous, or continuously singular. We further provide necessary and sufficient criteria for the finiteness of p-moments, p > 0 as well as exponential moments. In particular, a formula fo...