Fluctuations of Omega-killed spectrally negative Levy processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Li, Bo^1,2  Palmowski, Zbigniew³ 

[1] Nankai Univ, Dept Math, Tianjin, Peoples R China

[2] Nankai Univ, LPMC, Tianjin, Peoples R China

[3] Wroclaw Univ Sci & Technol, Fac Pure & Appl Math, Wyb Wyspianskiego 27, PL-50370 Wroclaw, Poland

关键词: Levy processes;    Omega model;    Occupation time;    Laplace transform;    Fluctuation theory;    Self-similar process;   

DOI  :  10.1016/j.spa.2017.10.018

来源: Elsevier

【 摘 要 】

In this paper we solve the exit problems for (reflected) spectrally negative Levy processes, which are exponentially killed with a killing intensity dependent on the present state of the process and analyze respective resolvents. All identities are given in terms of new generalizations of scale functions. For the particular cases omega(x) = q and omega(x) = q1((a, b))(x), we obtain results for the classical exit problems and the Laplace transforms of the occupation times in a given interval, until first passage times, respectively. Our results can also be applied to find the bankruptcy probability in the so-called Omega model, where bankruptcy occurs at rate omega(x) when the Levy surplus process is at level x < 0. Finally, we apply these results to obtain some exit identities for spectrally positive self-similar Markov processes. The main method throughout all the proofs relies on the classical fluctuation identities for Levy processes, the Markov property and some basic properties of a Poisson process. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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