A threshold-based risk process with a waiting period to pay dividends.

*(English)*Zbl 1412.60064Summary: In this paper, a modified dividend strategy is proposed by delaying dividend payments until the insurer’s surplus level remains at or above a threshold level \(b\) for a predetermined period of time \(h\). We consider two cases depending on whether the period of time sustained at or above level \(b\) is counted either consecutively or accumulatively (referred to as standard or cumulative waiting period). In both cases, we develop a recursive computational procedure to calculate the expected total discounted dividend payments made prior to ruin for a discrete-time Sparre Andersen renewal risk process. By varying the values of \(b\) and \(h\), a numerical study of the trade-off effects between finite-time ruin probabilities and expected total discounted dividend payments is investigated under a variety of scenarios. Finally, a generalized threshold-based strategy with a delayed dividend payment rule is studied under the compound binomial model.

##### MSC:

60G50 | Sums of independent random variables; random walks |

60K05 | Renewal theory |

91B30 | Risk theory, insurance (MSC2010) |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

##### Keywords:

discrete-time sparre Andersen renewal risk process; threshold strategy; waiting period; dividend payments; ruin probabilities; Parisian-type model; compound binomial model
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\textit{S. Drekic} et al., J. Ind. Manag. Optim. 14, No. 3, 1179--1201 (2018; Zbl 1412.60064)

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