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Some optimal dividends problems. (English) Zbl 1097.91040
The authors consider the classical compound Poisson surplus process modified by the introduction of a constant dividend barrier $$b$$. If the surplus reaches the level $$b$$, then the premium income no longer contributes to the surplus process but is paid out as dividends to shareholders. Main results include formulas for moments of arbitrary order $$n=1,2,\dots$$ for the present value $$D_u$$ at force of interest $$\delta$$ per unit time of dividends payable to shareholders until ruin occurs (given initial surplus $$u$$). In the special case $$\delta=0$$, the distribution of $$D_u$$ is derived. Results relating to the time and severity of ruin are presented. A discrete time model is investigated and three further modifications of the model are considered.

##### MSC:
 91B30 Risk theory, insurance (MSC2010)
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##### References:
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