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Risks 2018, 6(2), 33; https://doi.org/10.3390/risks6020033

Mixed Periodic-Classical Barrier Strategies for Lévy Risk Processes

1
Department of Probability and Statistics, Centro de Investigación en Matemáticas A.C. Calle Jalisco s/n. C.P. 36240, Guanajuato, Mexico
2
Department of Mathematics, Faculty of Engineering Science, Kansai University, 3-3-35 Yamate-cho, Suita-shi, Osaka 564-8680, Japan
*
Author to whom correspondence should be addressed.
Received: 25 February 2018 / Revised: 25 March 2018 / Accepted: 26 March 2018 / Published: 5 April 2018
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Abstract

Given a spectrally-negative Lévy process and independent Poisson observation times, we consider a periodic barrier strategy that pushes the process down to a certain level whenever the observed value is above it. We also consider the versions with additional classical reflection above and/or below. Using scale functions and excursion theory, various fluctuation identities are computed in terms of the scale functions. Applications in de Finetti’s dividend problems are also discussed. View Full-Text
Keywords: dividends; capital injection; Lévy processes; scale functions; fluctuation theory; excursion theory dividends; capital injection; Lévy processes; scale functions; fluctuation theory; excursion theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Pérez, J.-L.; Yamazaki, K. Mixed Periodic-Classical Barrier Strategies for Lévy Risk Processes. Risks 2018, 6, 33.

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