Summary
We show with a counterexample that the amount of the jumps of a claim number process may be different from one even if the usual condition on the right hand derivatives of the transition probabilities is fulfilled. We strengthen this condition in order to ensure the existenc of only jumps of amount one and we prove that the claim number process verifies a general Markov property provided some weak regularity assumptions on the transition probabilities are satisfied.
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Haezendonck, J. Some Mathematical Aspects of Claim Number Processes with the Markov Property. Blätter DGVFM 14, 579–584 (1980). https://doi.org/10.1007/BF02808718
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DOI: https://doi.org/10.1007/BF02808718