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 共查询到17条相似文献,搜索用时 125 毫秒
1.
考虑一种相依索赔风险模型,其中每次索赔发生时根据索赔额的大小可随机产生一延迟的副索赔.采用L ap lace变换方法,给出了索赔额服从轻尾分布时的最终破产概率,并研究了重尾分布时最终破产概率的极限上下界.  相似文献   

2.
一类索赔相依二元风险模型的破产概率问题研究   总被引:1,自引:0,他引:1  
考虑一种相依索赔风险模型,模型中假设每次主索赔可随机产生一延迟的副索赔,采用Laplacc变换方法,给出了索赔额服从轻尾分布时的最终破产概率,并研究了重尾分布时最终破产概率的渐进式.  相似文献   

3.
本文考虑随机利率下相依索赔的离散风险模型,模型中假设每次主索赔可能引起一次副索赔,而每次副索赔有可能延迟发生,当资产盈余达到边界b时,公司给投保者分发一定红利;考虑预期红利的现值时,假设利率服从一有限状态空间的马尔可夫链,我们得到了破产前预期累积分红所满足的差分方程及特殊索赔情形下预期累积分红现值的精确解析式,并结合实例进行了数值模拟.  相似文献   

4.
赵明清  张伟 《经济数学》2011,28(2):44-48
考虑了一类离散相依的风险模型,该模型假设主索赔以一定的概率引起两种副索赔,而第一种副索赔有可能延迟发生.通过引入一个辅助模型,分别得出了该风险模型初始盈余为0时破产前盈余与破产时赤字的联合分布的表达式、初始盈余为"时破产前盈余和破产时赤字的联合分布的递推公式、初始盈余为0时的破产概率,以及初始盈余为"时的破产概率求解方...  相似文献   

5.
考虑了具有常红利边界和延迟索赔的一类离散更新风险模型,其中间隔索赔到达时间从离散phase-type分布.定义了两种类型的索赔:主索赔和副索赔,主索赔以一定的概率引起副索赔且副索赔会以一定的概率被延迟到下一时段.通过引入辅助风险模型,推导了破产前红利折现期望满足的差分方程及其解.最后给出了当索赔额服从几何分布时的有关数值例子.  相似文献   

6.
研究一类索赔时间相依的二项风险模型,根据索赔额的大小随机产生一副索赔.通过引入辅助模型,运用概率论的分析方法得到了任意初始值μ下的Gerber-Shiu贴现罚函数,并求得了初始值为0时最终破产概率的明确表达式.最后结合保险实务进行了举例.  相似文献   

7.
主要研究了常数分红界下两离散相依险种风险模型的分红问题.模型假定一个险种的主索赔以一定的概率引起另外一险种的副索赔,且副索赔可能延迟发生,推导了到破产前一时刻为止累积分红折现均值满足的差分方程,并得到了特殊索赔额下累积分红折现均值的具体表达式,最后结合实际例子进行了数值模拟.  相似文献   

8.
相依索赔的二项风险模型的破产问题   总被引:1,自引:0,他引:1  
考虑一类相依索赔的二项风险模型,根据索赔额的大小随机产生一副索赔.通过引入辅助模型,研究相应模型生存概率的母函数,对任意的初始值u,得到了有限时间内生存概率的递推解,并结合保险实例进行了数值模拟.在某些特殊情形下得到有限时间生存概率和最终破产概率的明确表达式.  相似文献   

9.
本文研究了带一维扰动且含副索赔离散模型中的破产问题.利用递归等方法,得到了该模型下的破产前瞬时赢余和破产赤字联合分布的递推公式,以表明保险公司的破产严重状况,推广了不带扰动的风险模型中相应的结论.  相似文献   

10.
本文考虑一类具有延迟索赔的风险模型,模型中包含两种索赔,其中一种索赔可能延迟发生.在索赔额服从指数分布的情形下,建立此风险模型破产概率所满足的微分方程,得到破产概率的精确表达式,给出了数值模拟结果.  相似文献   

11.
The compound binomial risk model with time-correlated claims   总被引:1,自引:0,他引:1  
In this paper, we consider the compound binomial risk model with the time-correlated claims. It is assumed that every main claim will produce a by-claim but the occurrence of the by-claim may be delayed. We obtain the recursive formula of the joint distribution of the surplus immediately prior to ruin and deficit at ruin. Furthermore, the ruin probability is given by means of ruin probability and the deficit at ruin of the classical compound binomial risk model. Finally, we derive an upper bound for the ruin probability.  相似文献   

12.
Consider a continuous-time renewal risk model, in which every main claim induces a delayed by-claim. Assume that the main claim sizes and the inter-arrival times form a sequence of identically distributed random pairs, with each pair obeying a dependence structure, and so do the by-claim sizes and the delay times. Supposing that the main claim sizes with by-claim sizes form a sequence of dependent random variables with dominatedly varying tails, asymptotic estimates for the ruin probability of the surplus process are investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity.  相似文献   

13.
In this paper, we consider an extension to the compound Poisson risk model for which the occurrence of the claim may be delayed. Two kinds of dependent claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed with a certain probability. Both the expected discounted penalty functions with zero initial surplus and the Laplace transforms of the expected discounted penalty functions are obtained from an integro-differential equations system. We prove that the expected discounted penalty function satisfies a defective renewal equation. An exact representation for the solution of this equation is derived through an associated compound geometric distribution, and an analytic expression for this quantity is given for when the claim amounts from both classes are exponentially distributed. Moreover, the closed form expressions for the ruin probability and the distribution function of the surplus before ruin are obtained. We prove that the ruin probability for this risk model decreases as the probability of the delay of by-claims increases. Finally, numerical results are also provided to illustrate the applicability of our main result and the impact of the delay of by-claims on the expected discounted penalty functions.  相似文献   

14.
In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for K n claim amount distributions. Numerical illustrations are also given.  相似文献   

15.
We consider a compound Poisson surplus process perturbed by diffusion with debit interest. When the surplus is below zero or the company is on deficit, the company is allowed to borrow money at a debit interest rate to continue its business as long as its debt is at a reasonable level. When the surplus of a company is below a certain critical level, the company is no longer profitable, we say that absolute ruin occurs at this situation. In this risk model, absolute ruin may be caused by a claim or by oscillation. Thus, the absolute ruin probability in the model is decomposed as the sum of two absolute ruin probabilities, where one is the probability that absolute ruin is caused by a claim and the other is the probability that absolute ruin is caused by oscillation. In this paper, we first give the integro-differential equations satisfied by the absolute ruin probabilities and then derive the defective renewal equations for the absolute ruin probabilities. Using these defective renewal equations, we derive the asymptotical forms of the absolute ruin probabilities when the distributions of claim sizes are heavy-tailed and light-tailed. Finally, we derive explicit expressions for the absolute ruin probabilities when claim sizes are exponentially distributed.  相似文献   

16.
In this paper, we study a discrete time risk model with random interest rate. The convergence of the discounted surplus process is proved by using martingale techniques, an expression of ruin probability is obtained, and bounds for ruin probability are included. In the second part of the paper, the distribution of surplus immediately after ruin, the distribution of surplus just before ruin, the joint distribution of the surplus immediately before and after ruin, and the distribution of ruin time are discussed.  相似文献   

17.
Consider a compound Poisson surplus process of an insurer with debit interest and tax payments. When the portfolio is in a profitable situation, the insurer may pay a certain proportion of the premium income as tax payments. When the portfolio is below zero, the insurer could borrow money at a debit interest rate to continue his/her business. Meanwhile, the insurer will repay the debts from his/her premium income. The negative surplus may return to a positive level except that the surplus is below a certain critical level. In the latter case, we say that absolute ruin occurs. In this paper, we discuss absolute ruin quantities by defining an expected discounted penalty function at absolute ruin. First, a system of integro-differential equations satisfied by the expected discounted penalty function is derived. Second, closed-form expressions for the expected discounted total sum of tax payments until absolute ruin and the Laplace-Stieltjes transform (LST) of the total duration of negative surplus are obtained. Third, for exponential individual claims, closed-form expressions for the absolute ruin probability, the LST of the time to absolute ruin, the distribution function of the deficit at absolute ruin and the expected accumulated discounted tax are given. Fourth, for general individual claim distributions, when the initial surplus goes to infinity, we show that the ratio of the absolute ruin probability with tax to that without tax goes to a positive constant which is greater than one. Finally, we investigate the asymptotic behavior of the absolute ruin probability of a modified risk model where the interest rate on a positive surplus is involved.  相似文献   

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