Asymptotics for the sum of three state Markov dependent random variables
Volume 6, Issue 1 (2019), pp. 109–131
Pub. online: 19 November 2018
Type: Research Article
Open Access
Open Access
Received
10 August 2018
10 August 2018
Revised
11 October 2018
11 October 2018
Accepted
27 October 2018
27 October 2018
Published
19 November 2018
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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