An alternating risk reserve process - part I

Abstract

We consider an alternating risk reserve process with a threshold dividend strategy. The process can be in two different states and the state of the process can only change just after claim arrival instants. If at such an instant the capital is below the threshold, the system is set to state 1 (paying no dividend), and if the capital is above the threshold, the system is set to state 2 (paying dividend). Our interest is in the survival probabilities. In the case of exponentially distributed claim sizes, survival probabilities are found by solving a system of integro-differential equations. In the case of generally distributed claim sizes, they are expressed in the survival probabilities of the corresponding standard risk reserve processes