基于常利率投资和线性阈值分红策略下的绝对破产模型（英文）
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摘要
研究了常利率投资和线性阈值分红策略下的绝对破产模型,利用全概率公式、Taylor展式求解绝对破产前累计分红现值的矩母函数和n阶矩函数的更新方程,得到Gerber-Shiu期望折现罚金函数的偏微分方程表达式.
The paper mainly analyzes the absolute ruin risk model with constant interest investment and a linear threshold dividend strategy.By formula of full probability and Taylor expansion,renewal equations of moment-generating function and nth moment with present value of total dividends until absolution ruin are obtained.Further,partial integrodifferential equations of Gerber-Shiu function are given.
The paper mainly analyzes the absolute ruin risk model with constant interest investment and a linear threshold dividend strategy.By formula of full probability and Taylor expansion,renewal equations of moment-generating function and nth moment with present value of total dividends until absolution ruin are obtained.Further,partial integrodifferential equations of Gerber-Shiu function are given.
引文
[1]Cai J.On the time value of absolute ruin with debit interest[J].Advances in Applied Probability,2007,39(2):343-359.
[2]Peng D,Hou Z T,Liu Z M.The absolute ruin risk model with constant interest investment and a threshold dividend strategy[J].Acta Mathmaticae Applicatae Sinica,2012,35(5):885-866.
[3]Lin S X,Willmot G E,Drekic S.The classical risk model with a constant dividend barrier:Analysis of the Gerber-Shiu discounted penalty function[J].Insurance:Mathematics and Economics,2003,33(3):551-566.
[4]Lin X S,Pavlova K P.The compound Poisson risk model with a threshold dividend strategy[J].Insurance:Mathematics and Economics,2006,38(1):57-80.
[5]Gao S,Liu Z M.The perturbed compound poisson risk model with constant interest and a threshold dividend strategy[J].Journal of Computational and Applied Mathematics,2010,233(9):2181-2188.
[6]Albrecher H,Hartinger J,Tichy R F.On the distribution of dividend payments and the discounted penalty function in a risk model with linear dividend barrier[J].Scandinavian Actuarial Journal,2005,2005(2):103-126.
[7]Zhang Y,Kou B Y,Mao L.The ruin risk model with and a linear dividend strategy[J].Xi'an Industry University Journal(In Chinese),2015,35(1):8-15.
[8]Cramer H.On the Mathematical Theory of Risk[M].Stockholm:Skandia Jubilee Volume,1930.
[9]Yuan H L,Hu Y J.Absolute ruin in the compound Poisson risk model with constant dividend barrier[J].Statistics and Probability Letters,2008,78(14):2086-2094.
[10]Wang C W,Yin C C,Li E Q.On the classical risk model with credit and debit interests under absolute ruin[J].Statistics and Probability Letters,2010,80(15):427-436.
[11]Wan N.Dividend payments with a threshold strategy in the compound Poisson risk model perturbed by diffusion[J].Insurance:Mathematics and Economics,2007,40(3):509-523.
[2]Peng D,Hou Z T,Liu Z M.The absolute ruin risk model with constant interest investment and a threshold dividend strategy[J].Acta Mathmaticae Applicatae Sinica,2012,35(5):885-866.
[3]Lin S X,Willmot G E,Drekic S.The classical risk model with a constant dividend barrier:Analysis of the Gerber-Shiu discounted penalty function[J].Insurance:Mathematics and Economics,2003,33(3):551-566.
[4]Lin X S,Pavlova K P.The compound Poisson risk model with a threshold dividend strategy[J].Insurance:Mathematics and Economics,2006,38(1):57-80.
[5]Gao S,Liu Z M.The perturbed compound poisson risk model with constant interest and a threshold dividend strategy[J].Journal of Computational and Applied Mathematics,2010,233(9):2181-2188.
[6]Albrecher H,Hartinger J,Tichy R F.On the distribution of dividend payments and the discounted penalty function in a risk model with linear dividend barrier[J].Scandinavian Actuarial Journal,2005,2005(2):103-126.
[7]Zhang Y,Kou B Y,Mao L.The ruin risk model with and a linear dividend strategy[J].Xi'an Industry University Journal(In Chinese),2015,35(1):8-15.
[8]Cramer H.On the Mathematical Theory of Risk[M].Stockholm:Skandia Jubilee Volume,1930.
[9]Yuan H L,Hu Y J.Absolute ruin in the compound Poisson risk model with constant dividend barrier[J].Statistics and Probability Letters,2008,78(14):2086-2094.
[10]Wang C W,Yin C C,Li E Q.On the classical risk model with credit and debit interests under absolute ruin[J].Statistics and Probability Letters,2010,80(15):427-436.
[11]Wan N.Dividend payments with a threshold strategy in the compound Poisson risk model perturbed by diffusion[J].Insurance:Mathematics and Economics,2007,40(3):509-523.