Mathematics – Probability
Scientific paper
2011-10-22
Mathematics
Probability
48 pages, 3 figures
Scientific paper
In this paper we consider an optimal dividend problem for an insurance company which risk process evolves as a spectrally negative L\'{e}vy process (in the absence of dividend payments). We assume that the management of the company controls timing and size of dividend payments. The objective is to maximize the sum of the expected cumulative discounted dividends received until the moment of ruin and a penalty payment at the moment of ruin which is an increasing function of the size of the shortfall at ruin; in addition, there may be a fixed cost for taking out dividends. We explicitly solve the corresponding optimal control problem. The solution rests on the characterization of the value-function as the smallest stochastic super-solution that we establish. We find also an explicit necessary and sufficient condition for optimality of a single dividend-band strategy, in terms of a particular Gerber-Shiu function.
Avram Florin
Palmowski Zbigniew
Pistorius Martijn R.
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