Ruin probability for correlated negative risk sums model with Erlang processes

This paper studies a Sparre Andersen negative risk sums model in which the distribution of "interclaim" time is that of a sum of n independent exponential random variables. Thus, the Erlang(n) model is a special case. On this basis the correlated negative risk sums process with the common Erlang process is considered. Integro-differential equations with boundary conditions for I(u) are given. For some special cases a closed-form expression for I(u) is derived.