On Distributional Properties of Perpetuities

By Gerold Alsmeyer, Alexander Iksanov, Uwe Rösler. 2008

71 citations recorded by the source corpus.

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 for the abscissa of convergence of the moment generating function is provided. The results are illustrated with a number of examples at the end of the article.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/46a27d05d48c1f5061fc5f98f770045cef385434

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. M. Benaim
2. Florent Malrieu
3. Pierre-André Zitt
4. St'ephane Le Borgne
5. Claude Lobry

In Management Science and Operations Research

1. Florent Malrieu
2. M. Benaim
3. Theodore C. Bergstrom

Citations in the corpus

• Quantitative ergodicity for some switched dynamical systems (2012, methodology): “Many results are available both in the discrete time setting (see [26, 33, 21, 25, 1]) and in the continuous time setting (see [24, 16, 4]).”
• Long time behavior of diffusions with Markov switching (2009, unknown): “relies on precise estimates on the Laplace transform of Yt that can be derived from a discrete time model already studied in [6, 8, 1].”