The joint distribution of the Parisian ruin time and the number of claims until Parisian ruin in the classical risk model

In this paper we propose new iterative algorithm of calculating the joint distribution of the Parisian ruin time and the number of claims until Parisian ruin for the classical risk model. Examples are provided when the generic claim size is mixed Erlang distributed. We focus on the exponentially and the Erlang(k,μ) (k≥2k≥2) distributed claim sizes.