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A threshold-based risk process with a waiting period to pay dividends. (English) Zbl 1412.60064
Summary: 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
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