On Optimal Dividends in the Dual Model

Astin Bulletin, vol. 43, no. 3, 2013, pp 359 - 372

13 Pages Posted: 27 Feb 2014  

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Andreas E. Kyprianou

University of Bath

Kazutoshi Yamazaki

Kansai University - Department of Mathematics

Date Written: February 26, 2014

Abstract

We revisit the dividend payment problem in the dual model of Avanzi et al. Using the fluctuation theory of spectrally positive Levy processes, we give a short exposition in which we show the optimality of barrier strategies for all such Levy processes. Moreover, we characterize the optimal barrier using the functional inverse of a scale function. We also consider the capital injection problem 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 model, dividends, capital injections, spectrally positive Levy processes, scale functions

JEL Classification: C44, C61, G24, G32, G35

Suggested Citation

Bayraktar, Erhan and Kyprianou, Andreas E. and Yamazaki, Kazutoshi, On Optimal Dividends in the Dual Model (February 26, 2014). Astin Bulletin, vol. 43, no. 3, 2013, pp 359 - 372 . Available at SSRN: https://ssrn.com/abstract=2401630

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Andreas E. Kyprianou

University of Bath ( email )

Claverton Down
Bath, BA2 7AY
United Kingdom

Kazutoshi Yamazaki (Contact Author)

Kansai University - Department of Mathematics ( email )

3-3-35 Yamate-cho, Suita-shi
Osaka, 564-8680
Japan

HOME PAGE: http://https://sites.google.com/site/kyamazak/

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