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: Mat hematics and Economics 25, 63-84) to properties related to the joint and ma rginal moments of the time of ruin, the surplus before the time of ruin, an d 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 c ases when the claim size distribution is exponential, combinations of expon entials and mixtures of Erlangs. (C) 2000 Elsevier Science B.V. All rights reserved.