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.


91B30 Risk theory, insurance (MSC2010)
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