On a perturbed compound Poisson risk model under a periodic threshold-type dividend strategy

Abstract

In this paper, we model the insurance company's surplus flow by a perturbed compound Poisson model. Suppose that at a sequence of random time points, the insurance company observes the surplus to decide dividend payments. If the observed surplus level is larger than the maximum of a threshold b > 0 and the last observed level (after dividends payment if possible), then a fraction 0 < θ < 1 of the excess amount is paid out as a lump sum dividend. We assume that the solvency is also discretely monitored at these observation times, so that the surplus process stops when the observed value becomes negative. Integro-differential equations for the expected discounted dividend payments before ruin and the Gerber-Shiu expected discounted penalty function are derived, and solutions are also analyzed by Laplace transform method. Numerical examples are given to illustrate the applicability of our results.

On Periodic Dividends for the Classical Risk Model with Debit Interest

“…(9) can be obtained by using (6) and (7), while (11) is derived by (5) and (6). Let x � − c/α in (5), and we have boundary condition (12). □ Remark 1.…”

“…Considering the insurer monitors bankruptcy more closely than dividends, Avanzi et al [7] investigated periodic dividend barrier strategy in the dual model where the solvency is monitored continuously. For those risk models with periodic dividends and bankruptcy, the reader can refer to Zhang and Cheung [8,9], Avanzi et al [10], Dong et al [11], and Peng et al [12], among others. Different to the papers mentioned above, the periodic dividend strategy in Peng et al [12] is threshold strategy.…”

“…For those risk models with periodic dividends and bankruptcy, the reader can refer to Zhang and Cheung [8,9], Avanzi et al [10], Dong et al [11], and Peng et al [12], among others. Different to the papers mentioned above, the periodic dividend strategy in Peng et al [12] is threshold strategy. Now, we study surplus process (1) under periodic dividend strategy.…”

A Lévy Risk Model with Ratcheting Dividend Strategy and Historic High-Related Stopping

“…Under the framework of X, using Remark 3, we can get (13) immediately. (2) For x ∈ [0, b), we should consider whether the process will reach b before the first time of dropping across the level of the draw-down function of the running maximum.…”

“…To the best of our knowledge, the threshold dividend strategy, which is also known as the refracting dividend strategy, was firstly introduced by Jeanblanc-Picqué and Shiryaev [10] and Asmussen and Taksar [11] for the diffusion process, and by Gerber and Shiu [12], for the Cremér-Lundberg risk process. Recently, the periodic threshold dividend strategy under a perturbed compound Poisson model was studied in Peng et al [13] and Liu et al [14]. For original ideas and analogues of the threshold dividend strategy, the readers are referred to Gerber and Shiu [9] and Avanzi et al [15].…”