具有分红、流动储备金和利率的风险模型的绝对破产
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引用本文:张 燕1,2 , 赵培标2.具有分红、流动储备金和利率的风险模型的绝对破产[J].经济数学,2016,(2):15-22
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作者单位
张 燕1,2 , 赵培标2 (1.解放军理工大学 理学院, 南京 210094
2.南京理工大学 理学院, 南京 211101) 
中文摘要:建立了阈值分红策略下具有流动储备金、投资利率和贷款利率的复合泊松风险模型. 利用全概率公式和泰勒展式, 推导出了该模型的Gerber-Shiu函数和绝对破产时刻的累积分红现值期望满足的积分-微分方程及边界条件, 借助Volterra方程, 给出了Gerber-Shiu函数的解析表达式.
中文关键词:保险数学  Gerber-Shiu函数  积分—微分方程  分红  流动储备金
 
A Risk Model with Credit and Debit Interests, Liquid Reserves and Dividends Under Absolute Ruin
Abstract:This paper studied the compound Poisson risk model with liquid reserves, credit interest and debit interest in the presence of a threshold dividend strategy. By the total law of probability and Taylor's expansion, we first obtained the integro-differential equations with boundary conditions satisfying the Gerber-Shiu function and presented the closed form expressions for the Gerber-Shiu function. Secondly, we derived the integro-differential equations with boundary conditions satisfying the expected discounted present value of all dividends until absolute ruin by employing Volterra equations.
keywords:insurance mathematics  Gerber-Shiu function  integro-differential equation  dividend  liquid reserves
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