在这份报纸,期望的打折的惩罚功能与相关时间的主张在风险过程被考虑,也就是说,每个主要主张能引起一个由主张,但是由主张的出现可以被推迟。由更新参数,期望的值满足 integro 微分的方程的一个系统,这被显示出。而且,为期望的价值的 Laplace 变换的明确的表示借助于 Rouch 茅鈥檚 被导出定理。一个数字例子也为说明结果被给。
In this paper, the expected discounted penalty function is considered in the risk process with the time-correlated claims, that is, every main claim can cause a by-claim but the occurrence of the by-claim may be delayed. By the renewal argument, it is shown that the expected value satisfies a system of integro-differential equations. Moreover, the explicit expression for the Laplace transform of the expected value is derived by means of Rouche's theorem. A numerical example is also given for illustrating the result.