The distributions of the time to reach a given level and the duration of negative surplus in the Erlang(2) risk model

We study the distributions of [1] the first time that the surplus reaches a given level and [2] the duration of negative surplus in a Sparre Andersen risk process with the inter-claim times being Erlang(2) distributed. These distributions can be obtained through the inversion of Laplace transforms using the inversion relationship for the Erlang(2) risk model given by Dickson and Li (2010).