Distributional study of De Finetti's dividend problem for a general Levy insurance risk process

A E Kyprianou, Z Palmowski

Research output: Contribution to journalArticle

59 Citations (Scopus)

Abstract

We provide a distributional study of the solution to the classical control problem due to De Finetti (1957), Gerber (1969), Azcue and Muler (2005), and Avram et al. (2007), which concerns the optimal payment of dividends from an insurance risk process prior to ruin. Specifically, we build on recent work in the actuarial literature concerning calculations of the nth moment of the net present value of dividends paid out in the optimal strategy as well as the moments of the deficit at ruin and the Laplace transform of the red period. The calculations we present go much further than the existing literature, in that our calculations are valid for a general spectrally negative Lévy process as opposed to the classical Cramér--Lundberg process with exponentially distributed jumps. Moreover, the technique we use appeals principally to excursion theory rather than integro-differential equations and, for the case of the nth moment of the net present value of dividends, makes a new link with the distribution of integrated exponential subordinators.
Original languageEnglish
Pages (from-to)428-443
Number of pages16
JournalJournal of Applied Probability
Volume44
Issue number2
DOIs
Publication statusPublished - 2007

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