Асимптотика для суми трьох станів Маркова залежить від випадкових величин.
"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. Thesigned compound Poisson approximation is applied to the aggregate claims distribution after nNn?N periods. The accuracy of order O(n1)O(n1) and O(n1/2)O(n1/2) 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(n1)O(n1). The characteristic function method is used. The results can be applied to estimate the probable loss of an insurer to optimize an insurance premium".
