The moments of the time of ruin, the surplus before ruin, and the deficit at ruin

In this paper we extend the results in Lin and Willmot (1999 Insurance: Mathematics and Economics 25, 63–84) to properties related to the joint and marginal moments of the time of ruin, the surplus before the time of ruin, and the deficit at the time of ruin. We use an approach developed in Lin and Willmot (1999), under which the solution to a defective renewal equation is expressed in terms of a compound geometric tail, to derive explicitly the joint and marginal moments. This approach also allows for the establishment of recursive relations between these moments. Examples are given for the cases when the claim size distribution is exponential, combinations of exponentials and mixtures of Erlangs.