共查询到20条相似文献,搜索用时 31 毫秒
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Jun Yi GUO Kam C. YUEN Ming ZHOU 《数学学报(英文版)》2007,23(7):1281-1288
In this paper we consider risk processes with two classes of business in which the two claim-number processes are dependent Cox processes. We first assume that the two claim-number processes have a two-dimensional Markovian intensity. Under this assumption, we not only study the sum of the two individual risk processes but also investigate the two-dimensional risk process formed by considering the two individual processes separately. For each of the two risk processes we derive an expression for the ruin probability, and then construct an upper bound for the ruin probability. We next assume that the intensity of the two claim-number processes follows a Markov chain. In this case, we examine the ruin probability of the sum of the two individual risk processes. Specifically, a differential system for the ruin probability is derived and numerical results are obtained for exponential claim sizes. 相似文献
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A Markov risk model with two classes of insurance business is studied. In this model, the two classes of insurance business are independent. Each of the two independent claim number processes is the number of jumps of a Markov jump process from time 0 to t, whichever has not independent increments in general. An integral equation satisfied by the ruin probability is obtained and the bounds for the convergence rate of the ruin probability are given by using a generalized renewal technique. 相似文献
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Ruin theory with excess of loss reinsurance and reinstatements 总被引:1,自引:0,他引:1
The present paper studies the probability of ruin of an insurer, if excess of loss reinsurance with reinstatements is applied. In the setting of the classical Cramér-Lundberg risk model, piecewise deterministic Markov processes are used to describe the free surplus process in this more general situation. It is shown that the finite-time ruin probability is both the solution of a partial integro-differential equation and the fixed point of a contractive integral operator. We exploit the latter representation to develop and implement a recursive algorithm for numerical approximation of the ruin probability that involves high-dimensional integration. Furthermore we study the behavior of the finite-time ruin probability under various levels of initial surplus and security loadings and compare the efficiency of the numerical algorithm with the computational alternative of stochastic simulation of the risk process. 相似文献
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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
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一类带干扰风险过程的破产概率的估计 总被引:3,自引:0,他引:3
In this paper,a class of risk processes perturbed by diffusion are considered. The Lundberg inequalities for the ruin probability are obtained. The size of the Lundberg exponents for different kinds of risk model is compared. The numerical illustration for the impact of the parameters on the ruin probability is given. 相似文献
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In this paper, we consider a risk process with stochastic return on investments. The basic risk process is the classical risk process while the return on the investment generating process is a compound Poisson process plus a Brownian motion with positive drift. We obtain an integral equation for the ultimate ruin probability which is twice continuously differentiable under certain conditions. We then derive explicit expressions for the lower bound for the ruin probability. We also study a joint distribution related to exponential functionals of Brownian motion which is required in the derivations of the explicit expressions for the lower bound. 相似文献
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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
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Jing-min He Rong Wu Hua-yue Zhang 《应用数学学报(英文版)》2008,24(1):117-128
In this paper we mainly study the ruin probability of a surplus process described by a piecewise deterministic Markov process (PDMP). An integro-differential equation for the ruin probability is derived. Under a certain assumption, it can be transformed into the ruin probability of a risk process whose premiums depend on the current reserves. Using the same argument as that in Asmussen and Nielsen, the ruin probability and its upper bounds are obtained. Finally, we give an analytic expression for ruin probability and its upper bounds when the claim-size is exponentially distributed. 相似文献
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We investigate an insurance risk model that consists of two reserves which receive income at fixed rates. Claims are being requested at random epochs from each reserve and the interclaim times are generally distributed. The two reserves are coupled in the sense that at a claim arrival epoch, claims are being requested from both reserves and the amounts requested are correlated. In addition, the claim amounts are correlated with the time elapsed since the previous claim arrival.We focus on the probability that this bivariate reserve process survives indefinitely. The infinite-horizon survival problem is shown to be related to the problem of determining the equilibrium distribution of a random walk with vector-valued increments with ‘reflecting’ boundary. This reflected random walk is actually the waiting time process in a queueing system dual to the bivariate ruin process.Under assumptions on the arrival process and the claim amounts, and using Wiener–Hopf factorization with one parameter, we explicitly determine the Laplace–Stieltjes transform of the survival function, c.q., the two-dimensional equilibrium waiting time distribution.Finally, the bivariate transforms are evaluated for some examples, including for proportional reinsurance, and the bivariate ruin functions are numerically calculated using an efficient inversion scheme. 相似文献
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重尾索赔下的一类相依风险模型的若干问题 总被引:2,自引:2,他引:0
本文研究了重尾索赔下的一类相依风险模型,得到了破产概率的尾等价式及索赔盈余过程大偏差的渐近关系式.在该模型中,一索赔到达过程是Poisson过程,另一索赔到达过程为其p-稀疏过程. 相似文献
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利润最大化风险最小化是保险公司运营所追求的目标,破产概率为公司进行风险决策提供了依据。本文基于随机利率环境下,保费随公司盈余水平调整的双分红复合帕斯卡模型,研究了股份制保险公司的有限时间破产概率。我们证明了公司盈余过程的齐次马氏性,得到了有限时间破产概率的计算方法,最后给出了具体算例。 相似文献
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In this note,one kind of insurance risk models with the policies having multiple validity times are investigated.Explicit expressions for the ruin probabilities are obtained by using the martingale method.As a consequence,the obtained probability serves as an upper bound for the ruin probability of a newly developed entrance processes based risk model. 相似文献
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本文讨论马氏环境下带随机扰动的保单数量过程与索赔次数过程Cox相关的风险模型.利用鞅方 法,给出了该风险模型的破产概率的指数上界. 相似文献
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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 Gerber-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
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本文讨论了一类相关保险业务的风险过程,将相依索赔的风险过程转化为古典风险模型,得出最终破产概率的一般表达式. 相似文献
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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
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本研究了在常利率条件下普通更新风险模型的破产概率问题.采用一种递推的方法给出了这种情况下破产概率的一个上界估计. 相似文献
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经典风险模型只描述了单一险种的经营模式,具有局限性,本文对多险种的复合Poisson风险模型的破产概率进行了研究。本文给出了初始资本为0时破产概率皿(O)的明确表达式,以及理赔量服从指数分布且初始资本为u时破产概率ψ(u)的明确表达式。 相似文献