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On optimal dividends in the dual model

  • Erhan Bayraktar
  • Andreas Kyprianou
  • Kazutoshi Yamazaki

We revisit the dividend payment problem in the dual model of Avanzi et al. ([2], [1], and [3]). Using the fluctuation theory of spectrally positive L\'{e}vy processes, we give a short exposition in which we show the optimality of barrier strategies for all such L\'{e}vy processes. Moreover, we characterize the optimal barrier using the functional inverse of a scale function. We also consider the capital injection problem of [3] and show that its value function has a very similar form to the one in which the horizon is the time of ruin.

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Paper provided by in its series Papers with number 1211.7365.

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Date of creation: Nov 2012
Date of revision: Jun 2013
Handle: RePEc:arx:papers:1211.7365
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  1. Florin Avram & Zbigniew Palmowski & Martijn R. Pistorius, 2007. "On the optimal dividend problem for a spectrally negative L\'{e}vy process," Papers math/0702893,
  2. Biffis, Enrico & Kyprianou, Andreas E., 2010. "A note on scale functions and the time value of ruin for Lévy insurance risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 85-91, February.
  3. Avanzi, Benjamin & U. Gerber, Hans & S.W. Shiu, Elias, 2007. "Optimal dividends in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 111-123, July.
  4. repec:spr:compst:v:67:y:2008:i:1:p:21-42 is not listed on IDEAS
  5. Erhan Bayraktar & Masahiko Egami, 2007. "Optimizing Venture Capital Investments in a Jump Diffusion Model," Papers math/0703823,, revised Jul 2007.
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