A note on a class of delayed renewal risk processes

The Gerber-Shiu discounted penalty function is considered for a class of delayed renewal risk processes. Special cases of the model include the stationary renewal risk model and the situation where the time until the first claim is exponentially distributed. A mathematically tractable formula is derived for the Gerber-Shiu function, and consequently for quantities associated with the deficit at ruin, the surplus immediately prior to ruin, and the time of ruin.