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负二项分布的优良特性及其在风险管理中的应用 总被引:4,自引:2,他引:2
孟生旺.负二项分布的优良特性及其在风险管理中的应用.数理统计与管理,1998,17(2),9~12.负二项分布之所以在风险管理中被广泛应用是由其优良特性所决定的。本文主要讨论了其中三个方面的问题:第一,负二项分布在描述风险集体中任意风险的索赔次数时表现为伽玛分布对泊松分布按参数变化的加权平均;第二,负二项分布在描述某些风险的累积索赔额时具有复合泊松分布的形式;第三,负二项分布是当风险的索赔频率强度之间存在正向传染时索赔次数的分布 相似文献
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《数学的实践与认识》2015,(15)
考虑保险公司面临两类保险业务下的最优再保险问题.一类保险业务的索赔量分布波动较大,采用方差保费原理.而另一类索赔业务的索赔量分布比较集中,采用期望值保费原理.在净利润条件限制下,得到保险公司相应的最优比例和超额损失再保险策略. 相似文献
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本文对双险种风险模型,在一险种采取比例再保险,另一险种采取超出损失再保险策略下,得到调节系数与再保险自留水平之间的函数关系式,在理赔额为指数分布和Erlang(2)分布的条件下,得到最优比例再保险和超出损失再保险的自留水平,以及调节系数最大值。 相似文献
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本文在复合泊松跳索赔模型下,考虑保险公司投资于常弹性方差(CEV)金融市场和购买比例-超额损失组合再保险的最优策略.在期望效用最大化准则下,利用随机控制技巧,证明了,事实上,保险公司的最优再保险策略等同于要么购买一个纯超额损失再保险,要么购买一个纯比例再保险.进一步给出两种情形下的最优再保险和投资策略以及值函数的表达式. 相似文献
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讨论聚合风险的最优再保险问题,考虑n种索赔次数相关的险种构成的总体,在均值保费计算原理下的比例再保险模型。使得分出公司期望收益一定的情况下,以风险(方差表示)达到最小为目标函数而给出了最优分出比。 相似文献
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给出了二项分布、Poisson分布和几何分布高阶矩的递推公式,避免了其它计算方法上的不便与误差. 相似文献
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本文研究了一类带随机利率的离散时间比例再保险模型.运用递推方法,得到了破产前盈余、破产后赤字的分布以及它们的联合分布所满足的微分积分方程,作为推论得到了破产概率所满足的积分方程,推广了无再保险情形的结果. 相似文献
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Poisson random effect models with a shared random effect have been widely used in actuarial science for analyzing the number of claims. In particular, the random effect is a key factor in a posteriori risk classification. However, the necessity of the random effect may not be properly assessed due to the dual role of the random effect; it affects both the marginal distribution of the number of claims and the dependence among the numbers of claims obtained from an individual over time. We first show that the score test for the nullity of the variance of the shared random effect can falsely indicate significant dependence among the numbers of claims even though they are independent. To mitigate this problem, we propose to separate the dual role of the random effect by introducing additional random effects to capture the overdispersion part, which are called saturated random effects. In order to circumvent heavy computational issues by the saturated random effects, we choose a gamma distribution for the saturated random effects because it gives the closed form of marginal distribution. In fact, this choice leads to the negative binomial random effect model that has been widely used for the analysis of frequency data. We show that safer conclusions about the a posteriori risk classification can be made based on the negative binomial mixed model under various situations. We also derive the score test as a sufficient condition for the existence of the a posteriori risk classification based on the proposed model. 相似文献
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The Panjer (Katz) family of distributions is defined by a particular first-order recursion which is built on the basis of two parameters. It is known to characterize the Poisson, negative binomial and binomial distributions. In insurance, its main usefulness is to yield a simple recursive algorithm for the aggregate claims distribution. The present paper is concerned with the more general Lagrangian Katz family of distributions. That family satisfies an extended recursion which now depends on three parameters. To begin with, this recursion is derived through a certain first-crossing problem and two applications in risk theory are described. The distributions covered by the recursion are then identified as the generalized Poisson, generalized negative binomial and binomial distributions. A few other properties of the family are pointed out, including the index of dispersion, an extended Panjer algorithm for compound sums and the asymptotic tail behaviour. Finally, the relevance of the family is illustrated with several data sets on the frequency of car accidents. 相似文献
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In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer's arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends. 相似文献
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Fung-Yee Chan 《Insurance: Mathematics and Economics》1984,3(3):151-155
This paper gives a family of aggregate claims distributions using an integral equation representation. The Kernel of the integral equation is chosen so that the compound distributions such as Poisson and binomial are members of the same family. Furthermore, the aggregate claims distribution can be determined by the mean and variance of the number of claims. 相似文献
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从几何观点出发,利用二项式定理推导出自然数等幂和的一个新的通项递归公式,比已有的组合逼近式、递推式更简洁有效. 相似文献
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??Motivated by[1] and [2], we study in this
paper the optimal (from the insurer's point of view) reinsurance problem when
risk is measured by a general risk measure, namely the GlueVaR distortion risk
measures which is firstly proposed by [3].Suppose an insurer is exposed
to the risk and decides to buy a reinsurance contract written on the total
claim amounts basis, i.e. the reinsurer covers and the cedent covers
. In addition, the insurer is obligated to compensate the reinsurer
for undertaking the risk by paying the reinsurance premium,
( is the safety loading), under the expectation premium principle. Based
on a technique used in [2], this paper derives the optimal ceded loss
functions in a class of increasing convex ceded loss functions. It turns out
that the optimal ceded loss function is of stop-loss type. 相似文献
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A. Kyriakoussis H. Papageorgiou 《Annals of the Institute of Statistical Mathematics》1989,41(4):671-676
The conditional distribution of Y given X=x, where X and Y are non-negative integer-valued random variables, is characterized in terms of the regression function of X on Y and the marginal distribution of X which is assumed to be of a power series form. Characterizations are given for a binomial conditional distribution when X follows a Poisson, binomial or negative binomial, for a hypergeometric conditional distribution when X is binomial and for a negative hypergeometric conditional distribution when X follows a negative binomial. 相似文献