  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.
