On a discrete interaction risk model with delayed claims and randomized dividends

Abstract

In this paper, we study a discrete interaction risk model with delayed claims and randomized dividends payable at a non-negative threshold level. The recursive formula and the defective renewal equation for the Gerber-Shiu discounted penalty function are derived. Furthermore, the explicit expression for the discount-free Gerber-Shiu function is obtained. As an application, the joint distributions of the surplus immediately prior to ruin and the deficit at ruin and numerical illustration from a specific example are presented.