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

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 (2016) 基于常利率投资和线性阈值分红策略下的绝对破产模型。 统计学与应用, 5, 39-47. doi: 10.12677/SA.2016.51005

参考文献

[1] Cramer, H. (1930) On the Mathematical Theory of Risk. Skandia Jubillee Volume, Stockholm.

[2] Gerber, H.U. (1970) An Extension of the Renewal Equation and Its Application in the Collective Theory of Risk. Journal of Computational and Applied Mathematics, 3-4, 205-210. http://dx.doi.org/10.1080/03461238.1970.10405664

[3] Gerber, H.U. and Yang, H. (2007) Absolute Rain Probabilities in a Jump Diffusion Risk Model with Investment. North American Actuarial Journal, 11, 159-169. http://dx.doi.org/10.1080/10920277.2007.10597474

[4] Zeng, F.Z. and Xu, J.S. (2013) The Perturbed Dual Risk Model with Constant Interest and a Threshold Dividend Strategy. Abstract and Applied Analysis, 2013, Article ID: 981076. http://dx.doi.org/10.1155/2013/981076

[5] 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.

[6] De Finetti, B. (1957) Su un’impostazione alternativa dell teoria colletiva del rischio. Transactions of the XV International Congress of Actuaries, 2, 433-443.

[7] 张燕, 寇冰煜, 毛磊. 线性红利边界下带干扰的风险模型的破产理论[J]. 西安工业大学学报, 2015, 35(1): 8-15.

[8] 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. http://dx.doi.org/10.1016/j.cam.2010.10.034

[9] 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. http://dx.doi.org/10.1016/j.cam.2009.10.004

[10] Wan, N. (2007) Dividend Payments with a Threshold Strategy in the Compound Poisson Risk Model Perturbed by Diffusion. Insurance: Mathematics and Economics, 40, 509-523. http://dx.doi.org/10.1016/j.insmatheco.2006.08.002

[11] 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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