Approximations for the distribution of perpetuities with small discount rates

Abstract

Perpetuities (i.e., random variables of the form play an important role in many application settings. We develop approximations for the distribution of when the “accumulated short rate process”, , is small. We provide: (1) characterizations for the distribution of when and are driven by Markov processes; (2) general sufficient conditions under which weak convergence results can be derived for , and (3) Edgeworth expansions for the distribution of in the iid case and the case in which is a Levy process and the interest rate is a function of an ergodic Markov process.

Document Details

Document Type
Pub Defense Publication
Publication Date
May 18, 2022
Source ID
10.1002/nav.22058

Entities

People

  • Jose Blanchet
  • Peter W. Glynn

Organizations

  • Air Force Office of Scientific Research
  • National Science Foundation of Sri Lanka
  • Stanford University

Tags

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.