Differentiability of dividends function on jump-diffusion risk process with a barrier dividend strategy  

作　　者：Yuhua LU Rong WU 

机构地区：[1]School of Mathematics Sciences, Qufu Normal University, Qufu 273165, China [2]School of Mathematics Sciences and LPMC, Nankai University, Tianjin 300071, China

出　　处：《Frontiers of Mathematics in China》2014年第5期1073-1088,共16页中国高等学校学术文摘·数学（英文）

基　　金：Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11171179）.

摘　　要：We consider a dividends model with a stochastic jump perturbed by diffusion. First, we prove that the expected discounted dividends function is twice continuously differentiable under the condition that the claim distribution function has continuous density. Then we show that the expected discounted dividends function under a barrier strategy satisfies some integro-differential equation of defective renewal type, and the solution of which can be explicitly expressed as a convolution formula. Finally, we study the Laplace transform of ruin time on the modified surplus process.We consider a dividends model with a stochastic jump perturbed by diffusion. First, we prove that the expected discounted dividends function is twice continuously differentiable under the condition that the claim distribution function has continuous density. Then we show that the expected discounted dividends function under a barrier strategy satisfies some integro-differential equation of defective renewal type, and the solution of which can be explicitly expressed as a convolution formula. Finally, we study the Laplace transform of ruin time on the modified surplus process.

关 键 词：Expected discounted dividends ruin time integro-differentialequation Laplace transform barrier strategy 

分 类 号：O211.67[理学—概率论与数理统计] O174[理学—数学]