Frontiers of Mathematics in China >

2015 , Vol. 10 >Issue 2: 377 - 393

DOI: https://doi.org/10.1007/s11464-014-0409-z

RESEARCH ARTICLE

Gerber-Shiu function of a discrete risk model with and without a constant dividend barrier

  • Shanshan WANG , 1 ,
  • Chuangji AN 2 ,
  • Chunsheng ZHANG 2
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  • 1. Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
  • 2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China

Received date: 13 Jun 2013

Accepted date: 26 Jun 2014

Published date: 12 Feb 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We consider the discrete risk model with exponential claim sizes. We derive the finite explicit elementary expression for the joint density function of three characteristics: the time of ruin, the surplus immediately before ruin, and the deficit at ruin. By using the explicit joint density function, we give a concise expression for the Gerber-Shiu function with no dividends. Finally, we obtain an integral equation for the Gerber-Shiu function under the barrier dividend strategy. The solution can be expressed as a combination of the Gerber-Shiu function without dividends and the solution of the corresponding homogeneous integral equation. This latter function is given clearly by means of the Gerber-Shiu function without dividends.

Key words： Discrete risk model; Gerber-Shiu function; time of ruin; surplus before ruin; deficit at ruin; dividend

Cite this article

Shanshan WANG , Chuangji AN , Chunsheng ZHANG . Gerber-Shiu function of a discrete risk model with and without a constant dividend barrier[J]. Frontiers of Mathematics in China, 2015 , 10(2) : 377 -393 . DOI: 10.1007/s11464-014-0409-z

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