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Optimal dividend problem with a terminal value for spectrally positive Lévy processes. (English) Zbl 1290.91176

Summary: We consider a modified version of the classical optimal dividend problem taking into account both expected dividends and the time value of ruin. We assume that the risk process is modeled by a general spectrally positive Lévy process before dividends are deducted. Using the fluctuation theory of spectrally positive Lévy processes we give an explicit expression of the value function of a barrier strategy. Subsequently we show that a barrier strategy is the optimal strategy among all admissible ones. Our work is motivated by the recent work of E. Bayraktar et al. [Astin Bull. 43, No. 3, 359–372 (2013; Zbl 1283.91192)].

MSC:

91G50 Corporate finance (dividends, real options, etc.)
60G51 Processes with independent increments; Lévy processes
93E20 Optimal stochastic control

Citations:

Zbl 1283.91192
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References:

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