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Exit problems for jump processes with applicationsto dividend problems
YIN Chuancun *,SHEN Ying,WEN Yuzhen
School of Mathematical Sciences, Qufu Normal University, ShanDong QuFu 273165
*Correspondence author
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Funding: The National Natural Science Foundation of China（No.Grant No. 11171179）, the Research Fund for the Doctoral Program of Higher Education of China （No.No. 20093705110002）
Opened online:18 December 2012
Accepted by: none
Citation: YIN Chuancun,SHEN Ying,WEN Yuzhen.Exit problems for jump processes with applicationsto dividend problems[OL]. [18 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4502757
 
 
This paper investigates the first passage times to flat boundaries for hyper-exponential jump (diffusion) processes.Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the first passage times and undershoot (overshoot), the joint distribution of the process and running suprema (infima), are obtained. The processes recover many models appearing in the literature such as the compound Poisson risk models, the diffusion perturbed compound Poisson risk models, and their dual models. As applications, we present explicit expressions of the dividend formulae forbarrier strategy and threshold strategy.
Keywords:Applied probability; Jump diffusion; Compound Poisson process; First passage time; Hyper-exponential distribution; Dividend payment; Barrier strategy; Threshold strategy
 
 
 

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