共查询到18条相似文献,搜索用时 82 毫秒
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离散时间的双Poisson模型的破产概率 总被引:6,自引:0,他引:6
本文在离散复合Poisson风险模型的基础上,研究保费的收取也为一个Poisson过程的模型, 在保费收取量和理赔量都离散取整数值时,我们运用转移概率推导出了保险公司在有限时间内破产的概率以及最终破产概率的级数表达式和矩阵表达式. 相似文献
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对于一类推广的复合Poisson风险模型,利用破产概率所满足的一个瑕疵更新方程以及离散寿命分布类的性质获得了关于最终破产概率的函数型上界估计. 相似文献
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本文将双复合Poisson风险模型推广到资金利率和通货膨胀率下带干扰的新模型,运用鞅分析方法获得了其破产概率所满足的Lundberg不等式及其一般表达式。 相似文献
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本文给出了复合Poisson盈余过程在其个体理赔量服从两个指数分布的混合 分布时破产概率的显示解,并研究了此情形下破产概率的Lundberg界.作为应用,给出 了一种计算一般复合Poisson盈余过程破产概率的近似方法. 相似文献
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带干扰的双复合Poisson风险模型 总被引:1,自引:0,他引:1
对古典风险模型进行推广,主要研究保费收入过程为带干扰双复合Poisson过程的风险模型,运用鞅的方法得出了破产概率满足的Lundburg不等式. 相似文献
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该文将经典风险模型推广到非时齐复合Poisson风险模型.首先,运用经典方法和时变方法,计算了该模型下的破产特征量,且得到了更新方程的解析表达式.其次,定义了时变后相应模型的一个广义的Gerber-Shiu函数,验证了时变方法对非时齐Poisson风险模型的有效性.最后,当单次索赔量服从指数分布时,计算了相应的破产概率和Gerber-Shiu函数. 相似文献
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索赔次数为复合Poisson-Geometric过程的风险模型及破产概率 总被引:38,自引:1,他引:37
本文引入一类复合Poisson-Geometric分布,这类分布包括两个参数,是普通Poisson分布的一种推广,并在保险中有其实际的应用背景;基于此分布产生一个计数过程,称之为复合Poisson-Geometric过程.本文着重研究了索赔次数为复合Poisson-Geometric过程的风险模型,这种模型是经典风险模型的一个推广.针对此模型,本文给出了破产概率公式及更新方程.作为特例,当索赔额服从指数分布时,给出了破产概率的显式表达式. 相似文献
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双复合Poisson风险模型 总被引:14,自引:0,他引:14
研究了保费收取过程是复合Po isson过程,索赔总额是复合Po isson过程的风险模型,给出了不破产概率的积分表示,以及在特殊情况下不破产概率的具体表达式,并用鞅方法得出了破产概率满足的Lundberg不等式和一般公式. 相似文献
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Jun Cai Runhuan Feng Gordon E. Willmot 《Methodology and Computing in Applied Probability》2009,11(3):401-423
We modify the compound Poisson surplus model for an insurer by including liquid reserves and interest on the surplus. When
the surplus of an insurer is below a fixed level, the surplus is kept as liquid reserves, which do not earn interest. When
the surplus attains the level, the excess of the surplus over the level will receive interest at a constant rate. If the level
goes to infinity, the modified model is reduced to the classical compound Poisson risk model. If the level is set to zero,
the modified model becomes the compound Poisson risk model with interest. We study ruin probability and other quantities related
to ruin in the modified compound Poisson surplus model by the Gerber–Shiu function and discuss the impact of interest and
liquid reserves on the ruin probability, the deficit at ruin, and other ruin quantities. First, we derive a system of integro-differential
equations for the Gerber–Shiu function. By solving the system of equations, we obtain the general solution for the Gerber–Shiu
function. Then, we give the exact solutions for the Gerber–Shiu function when the initial surplus is equal to the liquid reserve
level or equal to zero. These solutions are the key to the exact solution for the Gerber–Shiu function in general cases. As
applications, we derive the exact solution for the zero discounted Gerber–Shiu function when claim sizes are exponentially
distributed and the exact solution for the ruin probability when claim sizes have Erlang(2) distributions. Finally, we use
numerical examples to illustrate the impact of interest and liquid reserves on the ruin probability.
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Conditions for the convexity of compound geometric tails and compound geometric convolution tails are established. The results are then applied to analyze the convexity of the ruin probability and the Laplace transform of the time to ruin in the classical compound Poisson risk model with and without diffusion. An application to an optimization problem is given. 相似文献
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《Insurance: Mathematics and Economics》2006,38(2):298-308
This paper considers a bivariate compound Poisson model for a book of two dependent classes of insurance business. We focus on the ruin probability that at least one class of business will get ruined. As expected, general explicit expressions for this bivariate ruin probability is very difficult to obtain. In view of this, we introduce the so-called bivariate compound binomial model which can be used to approximate the finite-time survival probability of the assumed model. We then study some simple bounds for the infinite-time ruin probability via the association properties of the bivariate compound Poisson model. We also investigate the impact of dependence on the infinite-time ruin probability by means of multivariate stochastic orders. 相似文献
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In this paper we investigate the ruin probability in a general risk model driven by a compound Poisson process. We derive a formula for the ruin probability from which the Albrecher–Hipp tax identity follows as a corollary. Then we study, as an important special case, the classical risk model with a constant force of interest and loss-carried-forward tax payments. For this case we derive an exact formula for the ruin probability when the claims are exponential and an explicit asymptotic formula when the claims are subexponential. 相似文献