We consider the Erlang(2) risk model and derive expressions for the density of the time to ruin and the joint density of the time to ruin and the deficit at ruin when the individual claim amount distribution is (i) an exponential distribution and (ii) an Erlang(2) distribution. We also consider...

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...

We derive a closed-form (infinite series) representation for the distribution of the ruin time for the Sparre Andersen model with exponentially distributed claims. This extends a recent result of Dickson et al. [Dickson, D.C.M., Hughes, B.D., Zhang, L., 2005. The density of the time to ruin...