The expected discounted penalty function for a kind of time-correlated risk model based on the renewal argument in consideration of the by-claim
In this paper, the expected discounted penalty function is considered in the risk process with the time-correlated claims, that is, every main claim can cause a by-claim but the occurrence of the by-claim may be delayed. By the renewal argument, it is shown that the expected value satisfies a system of integro-differential equations. Moreover, the explicit also given for illustrating the result.
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