  The paper deals with a generalization of the risk model with stochastic
premiums where dividends are paid according to a multi-layer dividend strategy.
First of all, we derive piecewise integro-differential equations for the
Gerber--Shiu function and the expected discounted dividend payments until ruin.
In addition, we concentrate on the detailed investigation of the model in the
case of exponentially distributed claim and premium sizes and find explicit
formulas for the ruin probability as well as for the expected discounted
dividend payments. Lastly, numerical illustrations for some multi-layer
dividend strategies are presented.
