Computing two actuarial quantities under multilayer dividend strategy with a constant interest rate: Based on Sinc methods

As risk processes with some kind of dividend strategies receive remarkable attention in the financial market, the analysis of risk quantities in the presence of interest (or return) has become an important issue in insurance risk theory, and the corresponding research should be of concern to actuaries. In this paper, we study a perturbed dual risk model with a constant interest rate and a multilayer threshold strategy. We derive respectively the integral differential equations satisfied by the expected present value of the total dividend until ruin and the Laplace transform at the time of ruin. By applying the Sinc method developed in this paper, we derive the approximate solutions of the integral differential equations satisfied by these two risk quantities. Finally, various numerical examples are provided to demonstrate the feasibility of the Sinc method.