Ruin Analysis of a Threshold Strategy in a Discrete-Time Sparre Andersen Model

In this paper, we extend the methodology of Alfa and Drekic (ASTIN Bull 37:293–317, 2007) 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.