The perturbed compound Poisson risk model with linear dividend barrier |
| |
Authors: | Donghai Liu Zaiming Liu |
| |
Affiliation: | a Department of Mathematics, Central South University, Changsha, Hunan 410075, PR Chinab Department of Mathematics, Hunan University of Science and Technology, Xiangtan, Hunan 411201, PR China |
| |
Abstract: | In this paper, we consider a diffusion perturbed classical compound Poisson risk model in the presence of a linear dividend barrier. Partial integro-differential equations for the moment generating function and the nth moment of the present value of all dividends until ruin are derived. Moreover, explicit solutions for the nth moment of the present value of dividend payments are obtained when the individual claim size distribution is exponential. We also provided some numerical examples to illustrate the applications of the explicit solutions. Finally we derive partial integro-differential equations with boundary conditions for the Gerber-Shiu function. |
| |
Keywords: | Linear dividend barrier Integro-differential equation Dividend payments Gerber-Shiu function |
本文献已被 ScienceDirect 等数据库收录! |
|