A process with stochastic claim frequency and a linear dividend barrier

The classical model of ruin theory is given by a Poisson claim number proce ss with single claims X-i and constant premium flow. Gerber has generalized this model by a linear dividend barrier b + at. Whenever the free reserve of the insurance reaches the barrier dividends are paid out in such a way t hat the reserve stays on the barrier The aim of this paper is to give a gen eralization of this model by using the idea of Reinhard. After an exponenti ally distributed time, the claim frequency changes to a different level, an d can change back again in the same way. This may be used e.g. in storm dam age insurance. The computations lead to systems of partial integro differen tial equations which are solved. (C) 1999 Elsevier Science B.V. All rights reserved.