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Generalized refracted Lévy process and its application to exit problem

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  • Noba, Kei
  • Yano, Kouji

Abstract

Generalizing Kyprianou–Loeffen’s refracted Lévy processes, we define a new refracted Lévy process which is a Markov process whose positive and negative motions are Lévy processes different from each other. To construct it we utilize the excursion theory. We study its exit problem and the potential measures of the killed processes. We also discuss approximation problem.

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  • Noba, Kei & Yano, Kouji, 2019. "Generalized refracted Lévy process and its application to exit problem," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1697-1725.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:5:p:1697-1725
    DOI: 10.1016/j.spa.2018.06.004
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    References listed on IDEAS

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    1. Chen, Zhen-Qing & Fukushima, Masatoshi, 2015. "One-point reflection," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1368-1393.
    2. Avram, Florin & Pérez, José-Luis & Yamazaki, Kazutoshi, 2018. "Spectrally negative Lévy processes with Parisian reflection below and classical reflection above," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 255-290.
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    Cited by:

    1. Irmina Czarna & Adam Kaszubowski, 2020. "Optimality of Impulse Control Problem in Refracted Lévy Model with Parisian Ruin and Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 982-1007, June.

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