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ON OPTIMAL DIVIDENDS IN THE DUAL MODEL

Published online by Cambridge University Press:  10 July 2013

Erhan Bayraktar ,
Andreas E. Kyprianou  and
Kazutoshi Yamazaki
Erhan Bayraktar*
Affiliation:
Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109-1043, USA
Andreas E. Kyprianou
Affiliation:
Department of Mathematical Sciences, The University of Bath, Claverton Down, Bath BA2 7AY, UK E-mail: a.kyprianou@bath.ac.uk
Kazutoshi Yamazaki
Affiliation:
Department of Mathematics, Faculty of Engineering Science, Kansai University, Suita-shi, Osaka 564-8680, Japan E-mail: kyamazak@kansai-u.ac.jp
*
E-mail: erhan@umich.edu
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Abstract

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We revisit the dividend payment problem in the dual model of Avanzi et al. ([2–4]). Using the fluctuation theory of spectrally positive Lévy processes, we give a short exposition in which we show the optimality of barrier strategies for all such Lévy processes. Moreover, we characterize the optimal barrier using the functional inverse of a scale function. We also consider the capital injection problem of [4] and show that its value function has a very similar form to the one in which the horizon is the time of ruin.

Keywords

Dual modeldividendscapital injectionsspectrally positive Lévy processesscale functions
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 3 , September 2013 , pp. 359 - 372
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © ASTIN Bulletin 2013

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