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