Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process

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On a general class of renewal risk process: analysis of the Gerber-Shiu function (2005, background): “…equation satisfied by the expected discounted penalty function is first derived and then solved to produce a defective renewal equation; see Gerber and Shiu (1998), Dickson (1998b), Dickson and Hipp (1998), (2001), Cheng and Tang (2003), Li and Garrido (2004), and Gerber and Shiu (2003), (2005).”
The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model (2007, background): “…solutions for f(x, y u) and f(y u) were studied when the distribution function of interclaim waiting times is (a) Erlang(2) (Dickson and Hipp 1998; Cheng and Tang 2003; Lin 2003); (b) Erlang (n) (Li and Garrido 2004); (c) phase-type (2) (Dickson and Hipp 2001; Dickson and Drekic 2004); (d)…”
On the discounted penalty function in a Markov-dependent risk model (2005, unknown): “(8) The matrix Aδ(s, u) is diagonally dominant for 0 ≤ u ≤ 1, since |cs− δ − λi + uλipi,ib̃i(s)| ≥ |δ + λi − cs| − |uλipi,ib̃i(s)| ≥ δ + λi − uλipi,ib̃i(0) > uλi(1 − pi,ib̃i(0)) = uλi ∑”
The discrete stationary renewal risk model and the Gerber-Shiu discounted penalty function (2004, background): “In these situations repeated differencing is needed, analogous to the continuous case considered by Cheng and Tang (2003), Gerber and Shiu (2003a,b), Li (2003), andLin (2003).”