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

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
[1] AMBAGASPITIYA R S. On the distribution of two classes of correlated aggregate claims[J]. Insurance: Mathematics and Economics, 1999, 24(3):301-308.
[2] AMBAGASPITIYA R S. On the distribution of a sum of correlated aggregate claims[J]. Insurance: Mathematics and Economics, 1998, 23(1):15-19.
[3] YUEN K C, GUO Junyi. Ruin probabilities for time-correlated claims in the compound binomial model[J]. Insurance: Mathematics and Economics, 2001, 29(1):47-57.
[4] XIAO Yuntao, GUO Junyi. The compound binomial risk model with time-correlated claims[J]. Insurance: Mathematics and Economics, 2007, 41(1):124-133.
[5] AMBAGASPITIYA R S. On the distribution of a sum of correlated aggregate claims[J]. Insurance: Mathematics and Economics, 1998, 23(1):15-19.
[6] ALBRECHER H J, BOXMA O J. A ruin model with dependence between claim sizes and claim intervals[J]. Insurance: Mathematics and Economics, 2004, 35:245-254.
[7] PAN Jie, WANG Guojing. Expected discounted penalty function for a thinning risk model[J]. Chinese Journal of Applied Probability and Statistics, 2009, 25(5):544-552.
[8] 黄玉娟,于广华. 稀疏过程下保费与理赔相关的风险模型的破产概率[J].山东大学学报:理学版,2011,46(7):56-59. HUANG Yujuan, YU Guanghua. Ruin probability for a risk model with dependence between premium and claim under the thinning process[J]. Journal of Shandong University: Natural Science, 2011, 46(7):56-59.
[9] BOIKOV A V. The Cramer-Lundberg model with stochastic premium process[J].Theory of Probability and its Application, 2003, 47(3):489-493.
[10] 陈珊萍,王过京,王振羽.稀疏过程在保险公司破产问题中的应用[J].数理统计与管理, 2001, 20(5):26-30. CHEN Shanping, WANG Guojing, WANG Zhenxu. The application of thinning process in risk problem[J].Chinese Journal of Application of Statistics and Management, 2001, 20(5):26-30.
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