Frontiers of Mathematics in China >

2014 , Vol. 9 >Issue 5: 1073 - 1088

DOI: 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 WU 2
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  • 1. School of Mathematics Sciences, Qufu Normal University, Qufu 273165, China
  • 2. School of Mathematics Sciences and LPMC, Nankai University, Tianjin 300071, China

Received date: 31 Oct 2012

Accepted date: 30 May 2013

Published date: 26 Aug 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Expected discounted dividends; ruin time; integro-differential equation; Laplace transform; barrier strategy

Cite this article

Yuhua LU , Rong WU . Differentiability of dividends function on jump-diffusion risk process with a barrier dividend strategy[J]. Frontiers of Mathematics in China, 2014 , 9(5) : 1073 -1088 . DOI: 10.1007/s11464-013-0313-y

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