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Ruin analysis of a threshold strategy in a discrete-time Sparre Andersen model. (English) Zbl 1245.91043
Summary: We extend the methodology of Alfa and Drekic [A. S. Alfa and S. Drekic, Astin Bull. 37, No. 2, 293–317 (2007; Zbl 1154.62076)] to analyze a discrete-time, delayed Sparre Andersen insurance risk model featuring a single threshold level and randomized dividend payments. Using matrix analytic techniques, we construct a set of computational procedures enabling one to calculate probability distributions associated with fundamental ruin-related quantities of interest, namely the time of ruin, the surplus immediately prior to ruin, and the deficit at ruin. Special cases of the general model, including the ordinary and stationary Sparre Andersen variants, are examined in several numerical examples.

MSC:
91B30 Risk theory, insurance (MSC2010)
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J22 Computational methods in Markov chains
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