A Note on Some New Perpetuities

Abstract

In a recent paper, Salminen and Yor (2004b) relate the distribution of the Dufresne's reflected perpetuity to the hitting time of a reflected Bessel process. In this contribution, we adapt the results of Salminen and Yor (2004b) in several ways. First, we use spectral theory to obtain a series expansion for the distribution that renders this quantity applicable to actuarial purposes. We also investigate perpetuities when the rate of return is modelled by a more general skew Brownian motion with drift.

Keywords: Skew Brownian motion, Bessel processes, local time, spectral theory, perpetuities