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A generalized penalty function for a class of discrete renewal processes. (English) Zbl 1277.60146
Summary: 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.

MSC:
60K10 Applications of renewal theory (reliability, demand theory, etc.)
60K15 Markov renewal processes, semi-Markov processes
62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
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