# On the discounted penalty function in the renewal risk model with general interclaim times

#### Abstract

The defective renewal equation satisfied by the Gerber-Shiu discounted penalty function in the renewal risk model with arbitrary interclaim times is analyzed. The ladder height distribution is shown to be a mixture of residual lifetime claim severity distributions, which results in an invariance property satisfied by a large class of claim amount models. In particular, when claims are exponentially distributed, a simple result follows when the penalty function is a function of the deficit only, and the Laplace transform of the (discounted) defective density of the surplus immediately prior to ruin is obtained. The simplified defective renewal equation which results when the penalty function only involves the deficit is used to obtain moments of the discounted deficit.

### Cite this paper

@inproceedings{Willmot2006OnTD, title={On the discounted penalty function in the renewal risk model with general interclaim times}, author={Gordon E. Willmot}, year={2006} }