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

doi:10.1007/s11464-013-0313-y

Front. Math. China

2014, Vol. 9

Issue (5) : 1073-1088 https://doi.org/10.1007/s11464-013-0313-y

RESEARCH ARTICLE

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

Yuhua LU^1,^*(

),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

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Abstract

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.

Keywords Expected discounted dividends ruin time integro-differential equation Laplace transform barrier strategy

Corresponding Author(s): Yuhua LU

Issue Date: 26 August 2014

Cite this article:

Yuhua LU,Rong WU. Differentiability of dividends function on jump-diffusion risk process with a barrier dividend strategy[J]. Front. Math. China, 2014, 9(5): 1073-1088.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-013-0313-y
https://academic.hep.com.cn/fmc/EN/Y2014/V9/I5/1073

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