A generalized penalty function for a class of discrete renewal processes

Abstract

Analysis of a generalized Gerber–Shiu function is considered in a discrete-time (ordinary) Sparre Andersen renewal risk process with time-dependent claim sizes. The results are then applied to obtain ruin-related quantities under some renewal risk processes assuming specific interclaim distributions such as a discrete K _n distribution and a truncated geometric distribution (i.e. compound binomial process). Furthermore, the discrete delayed renewal risk process is considered and results related to the ordinary process are derived as well.

Keywords:

• Discrete Sparre Andersen renewal risk process
• Discounted joint distribution
• Discrete K _n distribution
• Lagrange polynomials
• Compound binomial process
• Discrete delayed renewal process