Let , be independent identically distributed -valued random vectors. We prove a strong law of large numbers, a functional central limit theorem and a law of the iterated logarithm for the convergent perpetuities as . Under the standard actuarial interpretation, these results correspond to the situation when the actuarial market is close to the customer-friendly scenario of no risk.
A. Iksanov and I. Samoilenko were supported by the National Research Foundation of Ukraine (project 2020.02/0014 “Asymptotic regimes of perturbed random walks: on the edge of modern and classical probability”).
The authors thank the two anonymous referees for several useful comments. A. Iksanov thanks Alexander Marynych for a useful discussion concerning the proof of Lemma 5.4.
"Limit theorems for discounted convergent perpetuities." Electron. J. Probab. 26 1 - 25, 2021. https://doi.org/10.1214/21-EJP705