The risk model with stochastic premiums and a multi-layer dividend strategy
Volume 6, Issue 3 (2019), pp. 285–309
Pub. online: 28 August 2019
Type: Research Article
Open Access
Open Access
Received
29 March 2019
29 March 2019
Revised
4 August 2019
4 August 2019
Accepted
4 August 2019
4 August 2019
Published
28 August 2019
28 August 2019
Abstract
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.
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