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REFRACTION–REFLECTION STRATEGIES IN THE DUAL MODEL

Published online by Cambridge University Press:  03 October 2016

José-Luis Pérez  and
Kazutoshi Yamazaki
José-Luis Pérez
Affiliation:
Department of Probability and Statistics, Centro de Investigación en Matemáticas A.C. Calle Jalisco s/n. C.P. 36240, Guanajuato, Mexico, E-Mail: jluis.garmendia@cimat.mx
Kazutoshi Yamazaki*
Affiliation:
Department of Mathematics, Faculty of Engineering Science, Kansai University, 3-3-35 Yamate-cho, Suita-shi, Osaka 564-8680, Japan
*
E-Mail: kyamazak@kansai-u.ac.jp
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Abstract

We study the dual model with capital injection under the additional condition that the dividend strategy is absolutely continuous. We consider a refraction–reflection strategy that pays dividends at the maximal rate whenever the surplus is above a certain threshold, while capital is injected so that it stays non-negative. The resulting controlled surplus process becomes the spectrally positive version of the refracted–reflected process recently studied by Pérez and Yamazaki (2015). We study various fluctuation identities of this process and prove the optimality of the refraction–reflection strategy. Numerical results on the optimal dividend problem are also given.

Keywords

Dividendscapital injectionrefracted-reflected Lévy processesscale functionsdual model
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 1 , January 2017 , pp. 199 - 238
Copyright
Copyright © Astin Bulletin 2016 

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