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

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.