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Asymptotics for the sum of three state Markov dependent random variables
Volume 6, Issue 1 (2019), pp. 109–131
Gabija Liaudanskaitė   Vydas Čekanavičius  

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https://doi.org/10.15559/18-VMSTA123
Pub. online: 19 November 2018      Type: Research Article      Open accessOpen Access

Received
10 August 2018
Revised
11 October 2018
Accepted
27 October 2018
Published
19 November 2018

Abstract

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.

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Keywords
Signed compound Poisson approximation insurance model Markov chain Kolmogorov norm local norm total variation norm non-uniform estimate

MSC2010
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