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数学与物理
统计学与应用
Vol. 5 No. 1 (March 2016)
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基于常利率投资和线性阈值分红策略下的绝对破产模型
The Absolute Ruin Risk Model with Constant Interest Investment and a Linear Threshold Dividend Strategy
DOI:
10.12677/SA.2016.51005
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被引量
下载: 2,091
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国家自然科学基金支持
作者:
贺婷
,
吴黎军
:新疆大学数学与系统科学学院,新疆 乌鲁木齐
关键词:
线性分红阈值
;
绝对破产
;
常利率投资
;
更新方程
;
Gerber-Shiu期望折现罚金函数
;
Linear Threshold Dividend
;
Absolute Ruin Risk Model
;
Gerber-Shiu Function
;
Renewal Equation
摘要:
在本文中,我们研究基于常利率投资和线性阈值分红策略下的经典的绝对风险破产模型和带干扰的绝对破产风险模型问题。首先,本文得到累计分红现值的矩母函数和累计分红现值的n-阶矩函数的更新方程。然后,著名的Gerber-Shiu期望折现罚金函数所满足的更新方程及边界条件采用类似的方法也可以获得。
Abstract:
In this paper, the classical absolute ruin risk model and that model with interference are re-searched based on constant interest investment and a linear threshold barrier dividend strategy. First, renewal equations of moment-generating function and n-th moment with present value of total dividends until absolution ruin are obtained. Second, partial integro-differential equations of Gerber-Shiu function are given.
文章引用:
贺婷, 吴黎军. 基于常利率投资和线性阈值分红策略下的绝对破产模型[J]. 统计学与应用, 2016, 5(1): 39-47.
http://dx.doi.org/10.12677/SA.2016.51005
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http://dx.doi.org/10.1155/2013/981076
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彭丹, 侯振挺, 刘再明. 常利率和门限分红策略下带干扰的poisson风险模型的绝对破产模型问题[J]. 应用数学学报, 2012, 35(5): 885.
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Liu, D.H. and Liu, Z.M. (2011) The Perturbed Compound Poisson Risk Model with Linear Dividend Barrier. Journal of Computational and Applied Mathematics, 235, 2357-2363.
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Gao, S. and Liu, Z.M. (2010) The Perturbed Compound Poisson Risk Model with Constant Interest and a Threshold Dividend Strategy. Journal of Computational and Applied Mathematics, 233, 2181-2188.
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于文广. 保险风险模型的破产理论与分红策略的研究[D]: [博士学位论文]. 济南: 山东大学, 2014.
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