A Perturbed Risk Model with Liquid Reserves, Credit and Debit Interests and Dividends Under Absolute Ruin

Abstract

In this paper, we consider the dividend payments in the perturbed compound Poisson risk model with liquid reserves, credit interest and debit interest. It is assumed that an insurer is allowed to borrow money at some debit interest rate when his surplus is negative and he will keep the surplus as liquid reserves if the surplus is below a certain positive level. When the surplus attains this level, the excess of the surplus above this level will earn credit interest continuously at a constant interest rate. If the surplus continues to surpass a higher level, the excess of the surplus above this higher level will be paid out as dividends to shareholders. Integro-differential equations satisfied by the Geber-Shiu function are obtained, and the closed form expressions for the Geber-Shiu function are presented. Besides, we also derive the integro-differential equations with boundary conditions satisfied by the expected discounted present value of all dividends until absolute ruin.