The goal of this talk is to shed light on a connection between the probabilistic analysis of TCP protocols (used on the
Internet) and the exponential functional of a Levy (compound Poisson) process, which has received some attention in the mathematical finance literature. In that area, such functionals are known as perpetuities. We will first review the TCP application, and then derive several new distributional properties of perpetuities.

This talk is based on ongoing work with Krishanu Maulik (ISI, Calcutta) and the following papers:

Maulik, Krishanu; Zwart, Bert Tail asymptotics for exponential functionals of Levy processes. Stochastic Process. Appl. 116 (2006), no. 2, 156--177 Guillemin, Fabrice; Robert, Philippe; Zwart, Bert AIMD algorithms and exponential functionals. Ann. Appl. Probab. 14 (2004), no. 1, 90--117.