A risk process with delayed claims and constant dividend barrier

This article studies a risk process with constant dividend barrier where the delayed claims are considered, and two types of individual claims, main claims and by-claims, are defined. Each by-claim is induced by a main claim and may be delayed with a certain probability. Both the expected discounted penalty functions and the moment generating functions of the total dividend payments until ruin are derived. The moments of the total dividend payments until ruin and the dividends-penalty identity are given. Finally, numerical examples are provided to illustrate the applicability of the results and the effects of the delay probabilities on the expectations of the total dividend payments until ruin.