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Maximizing dividends without bankruptcy. (English) Zbl 1162.91375
Summary: Consider the classical compound Poisson model of risk theory, in which dividends are paid to the shareholders according to a barrier strategy. Let $$b^{*}$$ be the level of the barrier that maximizes the expectation of the discounted dividends until ruin. This paper is inspired by D. C. M. Dickson and H. R. Waters [Astin Bull. 34, No. 1, 49–74 (2004; Zbl 1097.91040)]. They point out that the shareholders should be liable to cover the deficit at ruin. Thus, they consider $$b^{0}$$, the level of the barrier that maximizes the expectation of the difference between the discounted dividends until ruin and the discounted deficit at ruin. In this paper, $$b^{*}$$ and $$b^{0}$$ are compared, when the claim amount distribution is exponential or a combination of exponentials.

##### MSC:
 91G50 Corporate finance (dividends, real options, etc.) 91B30 Risk theory, insurance (MSC2010)
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##### References:
 [1] Mathematical Methods in Risk Theory (1970) · Zbl 0209.23302 [2] Economics of Insurance (1990) [3] The Mathematical Theory of Insurance. (1974) [4] DOI: 10.1111/j.0960-1627.2005.00220.x · Zbl 1136.91016 · doi:10.1111/j.0960-1627.2005.00220.x [5] Stochastic Control in Insurance (2007) [6] Insurance: Mathematics and Economics 20 pp 215– (1997) [7] Numerical Analysis (1981) [8] An Introduction to Mathematical Risk Theory (1979) · Zbl 0431.62066 [9] Forthcoming in North American Actuarial Journal 10 (2006) [10] DOI: 10.1017/S0515036100013878 · doi:10.1017/S0515036100013878 [11] Insurance Risk and Ruin (2005) · Zbl 1060.91078 [12] Transactions of the XVth International Congress of Actuaries 2 pp 433– (1957) [13] Insurance: Mathematics and Economics 33 pp 551– (2003)
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