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 φ 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 φ.