JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (09): 78-83.doi: 10.6040/j.issn.1671-9352.0.2014.373

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Discounted penalty function for a thinning risk model with dividend

CHEN Jie1, LÜ Yu-hua2   

  1. 1. Department of Mathematics, Jining University, Jining 273155, Shandong, China;
    2. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China
  • Received:2014-08-14 Revised:2015-07-22 Online:2015-09-20 Published:2015-09-26

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Abstract: The thinning risk model with barrier dividend was considered. The integro-differential equation for the expected discounted penalty function was obtained. If the premium and the claim sizes are exponentially distributed, some expressions for the Laplace transform of the integro-differential equation were founded. When the premium and the claim sizes are exponentially distributed, the closed-form solutions of the time of ruin, the deficit at ruin and the surplus before ruin were obtained.

Key words: barrier dividend, Laplace transform, integro-differential equation, thinning process, expected discounted penalty function

CLC Number: 

  • O211.6
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