×

zbMATH — the first resource for mathematics

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)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Proceedings of the 6th International Congress on Insurance (2002)
[2] Transactions of the XVth International Congress of Actuaries 2 pp 433– (1957)
[3] Economics of Insurance (1990)
[4] Insurance: Mathematics & Economics 20 pp 1– (1997)
[5] Insurance: Mathematics & Economics 24 pp 51– (1999)
[6] Insurance: Mathematics & Economics 20 pp 215– (1997)
[7] DOI: 10.1080/10920277.1998.10595675 · Zbl 1081.91537 · doi:10.1080/10920277.1998.10595675
[8] Insurance: Mathematics & Economics 33 pp 551– (2003)
[9] Loss models – from data to decisions. (1998)
[10] Scandinavian Actuarial Journal pp 225– (2002)
[11] North American Actuarial Journal 8 pp 1– (2004)
[12] An Introduction to Mathematical Risk Theory (1979) · Zbl 0431.62066
[13] North American Actuarial Journal 2 pp 48– (1998)
[14] DOI: 10.2143/AST.21.2.2005364 · doi:10.2143/AST.21.2.2005364
[15] Scandinavian Actuarial Journal pp 105– (1984)
[16] Insurance: Mathematics & Economics 7 pp 1– (1988)
[17] Mathematical Methods in Risk Theory (1970) · Zbl 0209.23302
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.