Occupation times of spectrally negative Levy processes with applications

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Landriault, David²  Renaud, Jean-Francois¹  Zhou, Xiaowen³ 

[1] Univ Quebec, Dept Math, Montreal, PQ H2X 3Y7, Canada

[2] Univ Waterloo, Dept Stat & Actuarial Sci, Waterloo, ON N2L 3G1, Canada

[3] Concordia Univ, Dept Math & Stat, Montreal, PQ H3G 1M8, Canada

关键词: Occupation time;    Spectrally negative Levy processes;    Fluctuation theory;    Scale functions;    Ruin theory;   

DOI  :  10.1016/j.spa.2011.07.008

来源: Elsevier

【 摘 要 】

In this paper, we compute the Laplace transform of occupation times (of the negative half-line) of spectrally negative Levy processes. Our results are extensions of known results for standard Brownian motion and jump-diffusion processes. The results are expressed in terms of the so-called scale functions of the spectrally negative Levy process and its Laplace exponent. Applications to insurance risk models are also presented. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free