Asymptotics for the sum of three state Markov dependent random variables

The insurance model when the amount of claims depends on the state of the insured person (healthy, ill, or dead) and claims are connected in a Markov chain is investigated. The signed compound Poisson approximation is applied to the aggregate claims distribution after \(n\in \mathbb {N}\) periods. T...

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Bibliographic Details
Published in:arXiv.org 2020-01
Main Authors: Liaudanskaitė, Gabija, Čekanavičius, Vydas
Format: Article
Language:English
Subjects:
Characteristic functions
Dependent variables
Insurance
Markov chains
Norms
Random variables
Online Access:Get full text
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Summary:The insurance model when the amount of claims depends on the state of the insured person (healthy, ill, or dead) and claims are connected in a Markov chain is investigated. The signed compound Poisson approximation is applied to the aggregate claims distribution after \(n\in \mathbb {N}\) periods. The accuracy of order \(O(n^{-1})\) and \(O(n^{-1/2})\) is obtained for the local and uniform norms, respectively. In a particular case, the accuracy of estimates in total variation and non-uniform estimates are shown to be at least of order \(O(n^{-1})\). The characteristic function method is used. The results can be applied to estimate the probable loss of an insurer to optimize an insurance premium.
ISSN:2331-8422
DOI:10.48550/arxiv.2001.03320