Differentiability of dividends function on jump-diffusion risk process with a barrier dividend strategy
Yuhua LU1,*(),Rong WU2
1. School of Mathematics Sciences, Qufu Normal University, Qufu 273165, China 2. School of Mathematics Sciences and LPMC, Nankai University, Tianjin 300071, China
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.
. [J]. Frontiers of Mathematics in China, 2014, 9(5): 1073-1088.
Yuhua LU,Rong WU. Differentiability of dividends function on jump-diffusion risk process with a barrier dividend strategy. Front. Math. China, 2014, 9(5): 1073-1088.
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