an:05543695
Zbl 1166.60051
Loeffen, R. L.
An optimal dividends problem with a terminal value for spectrally negative L??vy processes with a completely monotone jump density
EN
J. Appl. Probab. 46, No. 1, 85-98 (2009).
00248386
2009
j
60J99 60G51 93E20
Levy process; stochastic control; divident problem; complete monotonicity
The author considers a modified version of the classical optimal dividends problem of de Finetti \ by adding to the objective function an extra term which takes account of the ruin time of the risk process, the latter being modeled by a spectrally negative L??vy process. It is shown that, in general, a barrier strategy is an optimal strategy under the condition that the L??vy measure has a completely monotone density. As a prerequisite, it is shown that under the latter condition, the \(q\)-scale function of a spectrally negative L??vy process has a derivative which is strictly non-convex.
Marius Iosifescu (Bucure??ti)