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2021 Limit theorems for discounted convergent perpetuities
Alexander Iksanov, Anatolii Nikitin, Igor Samoilenko
Author Affiliations +
Electron. J. Probab. 26: 1-25 (2021). DOI: 10.1214/21-EJP705

Abstract

Let (ξ1,η1), (ξ2,η2), be independent identically distributed R2-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 k0bξ1++ξkηk+1 as b1. 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.

Funding Statement

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”).

Acknowledgments

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.

Citation

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Alexander Iksanov. Anatolii Nikitin. Igor Samoilenko. "Limit theorems for discounted convergent perpetuities." Electron. J. Probab. 26 1 - 25, 2021. https://doi.org/10.1214/21-EJP705

Information

Received: 24 February 2021; Accepted: 13 September 2021; Published: 2021
First available in Project Euclid: 25 November 2021

Digital Object Identifier: 10.1214/21-EJP705

Subjects:
Primary: 60F15 , 60F17
Secondary: 60G50

Keywords: cluster set , functional central limit theorem , Law of the iterated logarithm , perpetuity , Strong law of large numbers

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