Finite-Time Expected Present Value of Operating Costs until Ruin in a Two-Dimensional Risk Model with Periodic Observation

This paper investigates ruin, capital injection, and dividends for a two-dimensional risk model. The model posits that surplus levels of insurance companies are governed by a perturbed composite Poisson risk model. This model introduces a dependence between the two surplus levels, present in both the associated perturbations and the claims resulting from common shocks. Critical levels of capital injection and dividends are established for each of the two risks. The surplus levels are observed discretely at fixed intervals, guiding decisions on capital injection, dividends, and ruin at these junctures. This study employs a two-dimensional Fourier cosine series expansion method to approximate the finite time expected discounted operating cost until ruin. The ensuing approximation error is also quantified. The validity and accuracy of the method are corroborated through numerical examples. Furthermore, the research delves into the optimal capital allocation problem.