Limit theorems for discounted convergent perpetuities

Iksanov, Alexander and Nikitin, Anatolii and Samoilenko, Igor (2021) Limit theorems for discounted convergent perpetuities. Electronic Journal of Probability, 26. ISSN 1083-6489

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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 ∑_k b^(ξ1+…+ξk)ηk+1 as b→1−. 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.

Item Type:	Article
Uncontrolled Keywords:	cluster set; functional central limit theorem; law of the iterated logarithm; perpetuity; strong law of large numbers
Subjects:	by fields of science > Mathematics
Divisions:	Educational and Scientific Institute of Information Technology and Business > Department of Economic-Mathematical Modeling and Information Technologies
Depositing User:	Anatolii Nikitin
Date Deposited:	20 Mar 2024 07:37
Last Modified:	20 Mar 2024 07:37
URI:	https://eprints.oa.edu.ua/id/eprint/9071

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