The Perturbed Dual Risk Model with Constant Interest and a Threshold Dividend Strategy

Abstract

We consider the perturbed dual risk model with constant interest and a threshold dividend strategy. Firstly, we investigate the moment-generation function of the present value of total dividends until ruin. Integrodifferential equations with certain boundary conditions are derived for the present value of total dividends. Furthermore, using techniques of sinc numerical methods, we obtain the approximation results to the expected present value of total dividends. Finally, numerical examples are presented to show the impact of interest on the expected present value of total dividends and the absolute ruin probability.

Numerical Ruin Probability in the Dual Risk Model with Risk-Free Investments

“…Contrary to the vast literature on the insurance models, there were very few results published in the dual model with constant force of interest. Zeng and Xu (2013) considered the perturbed dual risk model with constant interest and a threshold dividend strategy. They used the sinc method to approximate the expected present value of total dividends.…”