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On optimal periodic dividend and capital injection strategies for spectrally negative Lévy models

Part of: Stochastic systems and control Stochastic processes Mathematical economics

Published online by Cambridge University Press:  16 January 2019

Kei Noba ,
José-Luis Pérez ,
Kazutoshi Yamazaki  and
Kouji Yano
Kei Noba*
Affiliation:
Kyoto University
José-Luis Pérez*
Affiliation:
Centro de Investigación en Matemáticas
Kazutoshi Yamazaki*
Affiliation:
Kansai University
Kouji Yano*
Affiliation:
Kyoto University
*
* Postal address: Department of Mathematics, Graduate School of Science, Kyoto University Sakyo-ku, Kyoto 606-8502, Japan.
*** Postal address: Department of Probability and Statistics, Centro de Investigación en Matemáticas, A.C. Calle Jalisco s/n. C.P. 36240, Guanajuato, Mexico. Email address: jluis.garmendia@cimat.mx
**** Postal address: Department of Mathematics, Faculty of Engineering Science, Kansai University, 3-3-35 Yamate-cho, Suita-shi, Osaka 564-8680, Japan. Email address: kyamazak@kansai-u.ac.jp
* Postal address: Department of Mathematics, Graduate School of Science, Kyoto University Sakyo-ku, Kyoto 606-8502, Japan.
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Abstract

De Finetti’s optimal dividend problem has recently been extended to the case when dividend payments can be made only at Poisson arrival times. In this paper we consider the version with bail-outs where the surplus must be nonnegative uniformly in time. For a general spectrally negative Lévy model, we show the optimality of a Parisian-classical reflection strategy that pays the excess above a given barrier at each Poisson arrival time and also reflects from below at 0 in the classical sense.

Keywords

Dividendscapital injectionspectrally negative Lévy processscale functionperiodic barrier strategy

MSC classification

Primary: 91B30: Risk theory, insurance
Secondary: 60G51: Processes with independent increments; L'evy processes 93E20: Optimal stochastic control

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 4 , December 2018 , pp. 1272 - 1286
Copyright
Copyright © Applied Probability Trust 2018 

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