In the present paper, we give sufficient conditions for an ordering of De Pril approximations of the distribution of the number of claims in an insurance portfolio of independent policies. Possible extensions are discussed, both for the De Pril approximation and the Kornya approximation. A...

We study the distribution of the time to ruin in the classical risk model. We consider some methods of calculating this distribution...

Algorithms for the calculation of the distribution of the aggregate claimsfrom a life insurance portfolio have been derived by Kornya (1983), Hipp(1986) and De Pril (1986 and 1989)...

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 use probabilistic arguments to derive an expression for the joint density of the time to ruin and the number of claims until ruin in the classical risk model. From this we obtain a general expression for the probability function of the number of claims until ruin. We also consider the moments...

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...