How Many Claims to Get Ruined and Recovered?

We consider in the classical surplus process the number of claims occurring up to ruin, by a different method present by Stanford & Stroiñski. We consider the computation of Laplace transforms which can allow the computation of the probability function. Formulae presented are general.

The method uses the computation of the probability function of the number of claims during a negative excursion of the surplus process, in case it gets ruined. When initial surplus is zero this probability function allows us to completely define the recursion for the transform above. This uses the fact that in this particular case, conditional time to ruin has the same distribution as the time to recovery, given that ruin occurs.

We consider yet the computation of moments of the number of claims during recovery time, which with initial surplus zero allow us to compute the moments of the number of claims up to ruin.

Keywords: Probability of ruin; claim number up to ruin; claim number up to recovery; time to ruin; duration of negative surplus; severity of ruin; recursive methods.