Surplus analysis for a class of Coxian interclaim time distributions with applications to mixed Erlang claim amounts

Gerber–Shiu analysis with the generalized penalty function proposed by Cheung et al. (in press-a) is considered in the Sparre Andersen risk model with a K n family distribution for the interclaim time. A defective renewal equation and its solution for the present Gerber–Shiu function are derived, and their forms are natural for analysis which jointly involves the time of ruin and the surplus immediately prior to ruin. The results are then used to find explicit expressions for various defective joint and marginal densities, including those involving the claim causing ruin and the last interclaim time before ruin. The case with mixed Erlang claim amounts is considered in some detail.