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1.
In this paper,we consider the dividend problem in a two-state Markov-modulated dual risk model,in which the gain arrivals,gain sizes and expenses are influenced by a Markov process.A system of integrodifferential equations for the expected value of the discounted dividends until ruin is derived.In the case of exponential gain sizes,the equations are solved and the best barrier is obtained via numerical example.Finally,using numerical example,we compare the best barrier and the expected discounted dividends in the two-state Markov-modulated dual risk model with those in an associated averaged compound Poisson risk model.Numerical results suggest that one could use the results of the associated averaged compound Poisson risk model to approximate those for the two-state Markov-modulated dual risk model.  相似文献   

2.
In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, however, it can be Markovianized by introducing a supplementary process, We prove the Markov property of the related vector processes. Because such obtained processes belong to the class of the so-called piecewise-deterministic Markov process, the extended infinitesimal generator is derived, exponential martingale for the risk process is studied. The exponential bound of ruin probability in iafinite time horizon is obtained.  相似文献   

3.
In this paper we consider the risk process that is described by a piecewise deterministic Markov processes(PDMP).We first present the construction of the risk process and them discuss some ruin problems for this new kind of risk model.  相似文献   

4.
In this paper, we study a class of ruin problems, in which premiums and claims are dependent. Under the assumption that premium income is a stochastic process, we raise the model that premiums and claims are dependent, give its numerical characteristics and the ruin probability of the individual risk model in the surplus process. In addition, we promote the number of insurance policies to a Poisson process with parameter λ, using martingale methods to obtain the upper bound of the ultimate ruin probability.  相似文献   

5.
In this article, we construct an exponential martingale for the compound Poisson process with latent variableWith the help of this exponential martingale, we provide an asymptotic behavior of the coherent entropic risk measure for the compound Poisson process and a deviation inequality for the ruin probability of the partly shifted risk process.  相似文献   

6.
In this paper, we consider a compound Poisson risk model with taxes paid according to a loss-carry-forward system and dividends paid under a threshold strategy. First, the closed-form expression of the probability function for the total number of taxation periods over the lifetime of the surplus process is derived. Second, analytical expression of the expected accumulated discounted dividends paid between two consecutive taxation periods is provided. In addition, explicit expressions are also given for the exponential individual claims.  相似文献   

7.
We extend the classical compound Poisson risk model to the case where the premium income process, based on a Poisson process, is no longer a linear function. For this more realistic risk model, Lundberg type limiting results on the finite time ruin probabilities are derived. Asymptotic behaviour of the tail probabilities of the claim surplus process is also investigated.  相似文献   

8.
In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen(2000, P195, Proposition 1.10). The occupation time of non-dividend of this model is also discussed by means of Martingale method.  相似文献   

9.
We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Cerber-Shiu discounted penalty function. Then we give lower and upper bounds for the ruin probability. Finally, we present exact expressions for the ruin probability in a special case of renewal risk processes.  相似文献   

10.
In this paper, it is assumed that an insurer with a jump-diffusion risk process would invest its surplus in a bond market, and the interest structure of the bond market is assumed to follow the Vasicek interest model. This paper focuses on the studying of the ruin problems in the above compounded process. In this compounded risk model, ruin may be caused by a claim or oscillation. We decompose the ruin probability for the compounded risk process into two probabilities: the probability that ruin caused by a claim and the probability that ruin caused by oscillation. Integro-differential equations for these ruin probabilities are derived. When the claim sizes are exponentially distributed, the above-mentioned integro-differential equations can be reduced into a three-order partial differential equation.  相似文献   

11.
带干扰的多险种的风险模型   总被引:10,自引:0,他引:10  
保险公司往往会经营多种保险,用古典风险模型及其它推广的单一险种风险模型来研究其风险经营过程存在局限性,本讨论了带干扰的多险种风险模型,模型中保费的收人和理赔都是复合泊松过程,应用鞅论的方法,得出伦德伯格不等式和破产概率公式。  相似文献   

12.
广义复合二项风险模型下的破产概率   总被引:5,自引:0,他引:5  
将复合二项风险模型的保费收入推广为在单位时间内收取的保单数服从强度为α的poisson分布,利用鞅方法得出了其破产概率的一般公式及满足Lundberg不等式。  相似文献   

13.
本文从鞅条件出发 ,推导出了总理赔过程分别为复合 Poisson过程与复合二项过程 ,利率强度波动为带跳的 Poisson过程情形下的调节方程 ,并由此得到了一些有趣的结果。  相似文献   

14.
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   

15.
The paper considers the optimal dividend and capital injection strategies for the compound poisson risk process in a random interest rates environment. In the model, the surplus is assumed to be ordinary but the interest rates are governed by an exogenous Markov chain. Here, the problem is solved by two steps. First, we find out the capital injection form that the optimal strategy should follow. Then we look for the optimal solution in the restricted set with the particular capital injection form. In the paper, we discuss ``restricted' and ``unrestricted' two cases and provide a possible solution for ``unrestricted' case when the claim distribution is exponential.  相似文献   

16.
本文研究了一类保费与索赔均为批量到达的双险种破产模型,在特定的分布下导出了调节系数方程,得到了初始资本为u的破产概率的上界并与非批量到达的模型的破产上界进行了比较。  相似文献   

17.
钟朝艳 《经济数学》2011,28(1):85-88
考虑到保险公司在实际经营中收益所具有的不确定性和分红策略,建立一类具有线性红利界和带随机扰动的双复合Poisson风险模型,利用鞅方法给出模型关于破产概率的一个定理及上界.  相似文献   

18.
In this paper, we extend the classical compound binomial risk model to the case where the premium income process is based on a Poisson process, and is no longer a linear function. For this more realistic risk model, Lundberg type limiting results for the finite time ruin probabilities are derived. Asymptotic behavior of the tail probabilities of the claim surplus process is also investigated.  相似文献   

19.
保险系统中一种推广风险模型的破产概率   总被引:17,自引:0,他引:17  
将经典复合 Poisson风险模型推广至更为一般情况 ,其中保单以 Poisson分布流到达且收取的保费为随机变量 ,建立一种双复合 Poisson风险模型 .对此模型 ,得到了最终破产概率的一般表达式和破产概率的一个上界估计值 .  相似文献   

20.
徐俊科  刘再明  宋华 《经济数学》2007,24(3):234-238
本文对经典风险模型考虑有投资收益的情况.其投资收益率用泊松过程加布朗运动来描述.得到了罚金折现期望函数满足的方程.并对某些特殊情况给出了进一步的讨论.  相似文献   

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