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The perturbed compound Poisson risk model with constant interest and a threshold dividend strategy |
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| Authors: | Shan Gao Zaiming Liu |
| Institution: | a School of Mathematics, Central South University, Changsha, Hunan 410075, China b Department of Mathematics, Fuyang Normal College, Fuyang, Anhui 236032, China |
| Abstract: | In this paper, we consider the compound Poisson risk model perturbed by diffusion with constant interest and a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generation function and the nth moment of the present value of all dividends until ruin are derived. We also derive integro-differential equations with boundary conditions for the Gerber-Shiu functions. The special case that the claim size distribution is exponential is considered in some detail. |
| Keywords: | Brownian motion Constant interest Threshold dividend strategy Discounted dividend payments Gerber-Shiu discounted penalty function Integro-differential equation |
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