Ruin probabilities for time-correlated claims in the compound binomial model

In this paper we consider the ruin probability for a risk process with time-correlated claims in the compound binomial model. It is assumed that every main claim will produce a by-claim but the occurrence of the by-claim may be delayed. Recursive formulas for the finite time ruin probabilities are obtained and explicit expressions for ultimate ruin probabilities are given in two special cases.