| 常利息力下稀疏风险模型的生存概率 |
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| 引用本文： | 王贵红,赵金娥.常利息力下稀疏风险模型的生存概率[J].云南民族大学学报(自然科学版),2014(3):199-202. |
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| 作者姓名： | 王贵红 赵金娥 |
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| 作者单位： | [1]玉溪农业职业技术学院计算机科学系,云南玉溪653106 [2]红河学院数学学院,云南蒙自661199 |
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| 基金项目： | 国家自然科学基金（11301160）;云南省自然科学研究基金（2013FZ116）;云南省教育厅科学研究基金（2011C121）. |
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| 摘 要： | 对常利息力下的稀疏风险模型进行研究,其中保险公司的保费收入过程为一复合Poisson过程,而索赔计数过程是保单到达过程的p-稀疏过程.利用全概率公式及盈余过程的马氏性,得到了模型在有限时间内和无限时间内生存概率满足的积分-微分方程,并在保费额及索赔额均服从指数分布时得到了有限时间内生存概率的微分方程.
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| 关 键 词： | 常利息力 Poisson过程 稀疏过程 生存概率 积分-微分方程 |
Survival probability of the thinning risk model with a constant interest force |
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| WANG Gui-hong,ZHAO Jin-e.Survival probability of the thinning risk model with a constant interest force[J].Journal of Yunnan Nationalities University:Natural Sciences Edition,2014(3):199-202. |
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| Authors: | WANG Gui-hong ZHAO Jin-e |
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| Institution: | 2 Department of Computer Science, Yuxi Agricultural Vocation College, Yuxi 653106, China; 2. College of Mathematics, Honghe University, Mengzi 661199, China) |
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| Abstract: | In this paper, the thinning risk model with a constant interest force is discussed, in which the aggregate premium process is a compound Poisson process and the Claim number process is a p - thinning process of the pre- mium -arriving number process. The integral differential equations for the finite time survival probabihty and the infinite time survival probability are obtained in terms of the total probability formula and the strong Markov property of the surplus process. In addition, the differential equation of the finite time survival probability is obtained when the individual stochastic premium amount and claim amount are exponentially distributed. |
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| Keywords: | constant interest force Poisson process thinning process survival probability integral differential e-quation |
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