一类推广的常利率复合Poisson-Geometric风险模型的预警区问题
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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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