On the ruin probability for nonhomogeneous claims and arbitrary inter-claim revenues

Recently, Raducan et al. (2015) obtained recursive formulas for the ruin probability of a surplus process at or before claim instants under the assumptions that the claim sizes are independent, nonhomogeneous Erlang distributed, and independent of the inter-claim times (i.e., the times between two successive claims), which are assumed to be independent, identically distributed (i.i.d.), following an Erlang or a mixture of exponentials distribution. In this paper, we extend these formulas to the more general case when the inter-claim times are i.i.d. nonnegative random variables following an arbitrary distribution. We also present numerical results based on the new recursions, discuss some computational aspects and state a conjecture that connects the ordering of the claims arrival with the magnitude of the corresponding ruin probabilities.