Spectrally negative Levy processes with Parisian reflection below and classical reflection above

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Avram, Florin¹  Perez, Jose-Luis²  Yamazaki, Kazutoshi³ 

[1] Univ Pau, Lab Math Appl, Pau, France

[2] Ctr Invest Matemat, Dept Probabil & Stat, AC Calle Jalisco S-N, Guanajuato 36240, Mexico

[3] Kansai Univ, Fac Engn Sci, Dept Math, 3-3-35 Yamate Cho, Suita, Osaka 5648680, Japan

关键词: Capital injections;    Dividends;    Scale functions;    Levy processes;    Excursion theory;   

DOI  :  10.1016/j.spa.2017.04.013

来源: Elsevier

【 摘 要 】

We consider a company that receives capital injections so as to avoid ruin. Differently from the classical bail-out settings, where the underlying process is restricted to stay at or above zero, we study the case bail-out can only be made at independent Poisson observation times. Namely, we study a version of the reflected process that is pushed up to zero only on Poisson arrival times at which the process is below zero. We also study the case with additional classical reflection above so as to model a company that pays dividends according to a barrier strategy. Focusing on the spectrally negative Levy case, we compute, using the scale function, various fluctuation identities, including capital injections and dividends. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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