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.
Highlights
The ruin measures such as the ruin probability, the surplus prior to ruin and the deficit at ruin have attracted great interest of researchers recently
For the classical risk model and its different generalizations, different dividend strategies have been studied in a number of papers
Developing a recursive algorithm to calculate the moments of the expected discounted dividend payments for a class of risk models with Markovian claim arrivals, Badescu and Landriault [3] generalize some of the results obtained in [1]
Summary
The ruin measures such as the ruin probability, the surplus prior to ruin and the deficit at ruin have attracted great interest of researchers recently (see, e.g., [2, 28, 33] and references therein). Developing a recursive algorithm to calculate the moments of the expected discounted dividend payments for a class of risk models with Markovian claim arrivals, Badescu and Landriault [3] generalize some of the results obtained in [1] (see [4] for some results related to the class of Markovian risk models with a multi-layer dividend strategy). The absolute ruin problem in the classical risk model with constant interest force and a multi-layer dividend strategy is investigated in [43], where a piecewise integrodifferential equation for the discounted penalty function is derived, some explicit expressions are given when claims are exponentially distributed and an asymptotic formula for the absolute ruin probability is obtained for heavy-tailed claim sizes.
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