Blanchet, J., & Glynn, P. (2023). Approximations for the distribution of perpetuities with small discount rates. Naval Research Logistics (NRL), 70(5), 454-471. https://doi.org/10.1002/nav.22058
Abstract
Perpetuities (i.e., random variables of the form D=∫0∞e−Γ(t−)dΛ(t)$$ D={\int}_0^{\infty }{e}^{-\Gamma \left(t-\right)}d\Lambda (t) $$ play an important role in many application settings. We develop approximations for the distribution of D$$ D $$ when the “accumulated short rate process”, Γ$$ \Gamma $$, is small. We provide: (1) characterizations for the distribution of D$$ D $$ when Γ$$ \Gamma $$ and Λ$$ \Lambda $$ are driven by Markov processes; (2) general sufficient conditions under which weak convergence results can be derived for D$$ D $$, and (3) Edgeworth expansions for the distribution of D$$ D $$ in the iid case and the case in which Λ$$ \Lambda $$ is a Levy process and the interest rate is a function of an ergodic Markov process.
Authors
Jose Blanchet, Peter Glynn
Publication date
2023/8
Journal
Naval Research Logistics (NRL)
Volume
70
Issue
5
Pages
454-471
Publisher
John Wiley & Sons, Inc.
