Some results on absolute ruin in the perturbed insurance risk model with investment and debit interests

In this paper, we consider a perturbed compound Poisson risk model with investment and debit interests. Dividends are paid to the shareholders according to a threshold dividend strategy. An alternative assumption is that when the surplus is negative, a debit interest is applied and when the surplus is above a certain positive level, the insurer could earn investment interest. Integro-differential equations with boundary conditions satisfied by the moment-generating function, the nth moment of the present value of all dividends until absolute ruin and the Gerber–Shiu expected discounted penalty function are obtained. Then, we present the explicit expressions for the zero discounted nth moment of the present value of all dividends until absolute ruin in the case of exponential claims. Finally, numerical example is also given to illustrate the effect of the related parameters on the first moment of the present value of all dividends until absolute ruin.