一类推广的常利率复合Poisson-Geometric风险模型的预警区问题

赵明清; 尚 鹂; 李 田

一类推广的常利率复合Poisson-Geometric风险模型的预警区问题

引用本文：赵明清, 尚鹂, 李田.一类推广的常利率复合Poisson-Geometric风险模型的预警区问题[J].经济数学,2015,(1):1-5

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作者	单位
赵明清, 尚鹂, 李田	（山东科技大学数学与系统科学学院，山东青岛 266590）

中文摘要:在复合Poisson-Geometric风险模型的基础上，引入利率因素，并将保费收入由线性过程推广为复合Poisson过程，建立了一类推广的带常利率复合Poisson-Geometric风险模型，该模型描述现实的能力更强，更具有实际意义.然后，利用盈余过程的强马氏性推导出了首个预警区的条件矩母函数所满足的积分方程，并进一步在保费额和索赔额都服从指数分布的情形下得出了其解析解.

中文关键词:预警区复合Poisson-Geometric风险模型常利率条件矩母函数

Duration of Negative Surplus for a Generalized Compound Poisson-Geometric Risk Model with Constant Interest Rate

Abstract:On the basis of the compound Poisson-Geometric risk model, by introducing interest rate and extending the Premium income from linear to compound Poisson process, this paper set up a Generalized Compound Poisson-Geometric Risk Model with Constant Interest Rate. The ability of the model to describe the realistic is more stronger. At the same time, it has more practical significance. Then taking full advantage of the strong Markov property of the surplus process, an integral differential function for the first duration of negative surplus was obtained. Finally, the explicit expression was given when the Premium and the claim were exponential distributions.

keywords:duration of negative surplus compound Poisson-Geometric risk model constant interest rate conditional moment generating function

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