On the time to ruin for Erlang(2) risk processes

In this paper, we consider a Sparre Andersen risk process for which the claim inter-arrival distribution is Erlang(2). Our purpose is to find expressions for moments of the time to ruin, given that ruin occurs. To do this, we define an auxiliary function phi along the lines of Gerber and Shiu [N. Am. Actu. J. 2 (1998) 48] and Gerber and Landry [Ins.: Math. Econ. 22 (1998) 263]. Our method of solution differs from that of Willmot and Lin [Ins.: Math. Econ. 25 (1999) 570; Ins.: Math. Econ. 27 (2000) 19] who consider this problem for the classical risk model, in that we first solve for the auxiliary function phi. (C) 2001 Elsevier Science BN. All rights reserved.