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具有马氏调制费率的复合Poisson风险模型的破产概率 总被引:1,自引:0,他引:1
对于给定的初始状态和初始分布 ,本文分别给出了条件破产概率 Ψi(u)和最终破产概率 Ψ(u)所满足的积分方程 ,并给出了零初始资产时破产概率 Ψ(0 )的明确表达式 . 相似文献
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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
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完全离散的经典风险模型 总被引:32,自引:1,他引:31
本文系统地探讨了完全离散的经典风险模型,特别是重点研究了与风险有关的最终破产概率,破产前一刻的盈余和破产时赤字的概率律.Gerber仅在初始盈余为零的情况下给出了上述概率律的显式解,本文则对任意的初始盈余u≥0,给出了上述概率或概率律的递推解、变换解与显式解. 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
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完全离散经典风险模型中的渐近解和Lundberg型不等式 总被引:26,自引:0,他引:26
研究完全离散经典风险模型,在调节系数存在前提下,借助离散更新方程的一个极限定理,对于充分大的初始盈余导出了最终破产概率,破产前一刻的盈余和破产时赤字的概率规律的渐近解,此外,还对任意的初始盈余值,利用鞅论技巧导出了最母破产概率的一个Lundberg型上界。 相似文献
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复合二项风险模型的破产概率 总被引:3,自引:0,他引:3
本首次讨论了一般情形的复合二项风险模型,考虑了它的一些有关性质,得出了初始资本的0时的破产概率,它只与安全负荷系数有关,最后得出了初始资本为u≥0的情况下的破产概率的一般公式。 相似文献
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一类多险种风险过程的破产概率 总被引:49,自引:0,他引:49
由于保险公司风险经营规模的不断扩大,考虑到用单一险种的风险模型来描述风险经营过程的局限性,本文建立了多险种风险模型,并对其中一类特殊的风险模型的破概率进行了研究,给出了初始资本为0时破产概率Ψ(0)的明确表达式,以及初始资本为μ的破产概率Ψ(μ)的近似估计和在某些特殊情形下Ψ(μ)的明确表达式。 相似文献
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In this paper, for a kind of risk models with heavy-tailed and delayed claims, we derive the asymptotics of the infinite-time ruin probability and the uniform asymptotics of the finite-time ruin probability. The numerical simulation results are also presented. The results of theoretical analysis and numerical simulation
show that the influence of the delay for the claim payment is nearly negligible to the ruin probability when the initial capital and running-time are all large. 相似文献
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Li Wei 《应用数学学报(英文版)》2008,24(4):649-654
Considering the classical model with risky investment, we are interested in the ruin probability that is minimized by a suitably chosen investment strategy for a capital market index. For claim sizes with common distribution of extended regular variation, starting from an integro-differential equation for the maximal survival probability, we find that the corresponding ruin probability as a function of the initial surplus is also extended regular variation. 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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Stéphane Loisel 《Insurance: Mathematics and Economics》2008,42(2):746-762
We consider the classical risk model and carry out a sensitivity and robustness analysis of finite-time ruin probabilities. We provide algorithms to compute the related influence functions. We also prove the weak convergence of a sequence of empirical finite-time ruin probabilities starting from zero initial reserve toward a Gaussian random variable. We define the concepts of reliable finite-time ruin probability as a Value-at-Risk of the estimator of the finite-time ruin probability. To control this robust risk measure, an additional initial reserve is needed and called Estimation Risk Solvency Margin (ERSM). We apply our results to show how portfolio experience could be rewarded by cut-offs in solvency capital requirements. An application to catastrophe contamination and numerical examples are also developed. 相似文献
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对索赔为复合Poisson-Geometric过程的双险种风险模型进行研究,给出了当初始资本为0及索赔额为指数分布下破产概率的具体表达式,并利用鞅方法得到了最终破产概率满足的Lundberg不等式和一般公式. 相似文献