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1.
In this paper we study the tail behaviour of the probability of ruin within finite time t, as initial risk reserve x tends to infinity, for the renewal risk model with strongly subexponential claim sizes. The asymptotic formula holds uniformly for t∈[f(x), ∞), where f(x) is an infinitely increasing function, and substantially extends the result of Tang (Stoch. Models 2004; 20 :281–297) obtained for the class of claim distributions with consistently varying tails. Two examples illustrate the result. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
2.
We consider a nonstandard risk model with constant interest rate. For the case where the claim sizes follow a common heavy-tailed
distribution and fulfill a dependence structure proposed by Geluk and Tang [J. Geluk and Q. Tang, Asymptotic tail probabilities
of sums of dependent subexponential random variables, J. Theor. Probab., 22:871–882, 2009] while the interarrival times fulfill the so-called widely lower orthant dependence, we establish a weakly
asymptotically equivalent formula for the infinite-time ruin probability. In particular, when the dependence structure for
claim sizes is strengthened to the widely upper orthant dependence, this result implies a uniformly asymptotically equivalent
formula for the finite-time and infinite-time ruin probabilities. 相似文献
3.
In this article, some asymptotic formulas of the finite-time ruin probability for a two-dimensional renewal risk model are obtained. In the model, the distributions of two claim amounts belong to the intersection of the long-tailed distributions class and the dominated varying distributions class and the claim arrival-times are extended negatively dependence structures. Assumption that the claim arrivals of two classes are governed by a common renewal counting process. The asymptotic formulas hold uniformly for t ∈ [f(x), ∞), where f(x) is an infinitely increasing function. 相似文献
4.
The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims 总被引:2,自引:0,他引:2
Recently, Tang [Tang, Q., 2005a. Asymptotic ruin probabilities of the renewal model with constant interest force and regular variation. Scand. Actuar. J. (1), 1–5] obtained a simple asymptotic formula for the ruin probability of the renewal risk model with constant interest force and regularly varying tailed claims. In this paper, we use a completely different approach to extend Tang’s result to the case in which the claims are pairwise negatively dependent and extended regularly varying tailed. 相似文献
5.
In this paper, we consider the random sums of i.i.d. random variables ξ
1,ξ
2,... with consistent variation. Asymptotic behavior of the tail P(ξ1 + ... + ξη > x), where η is independent of ξ
1,ξ
2,..., is obtained for different cases of the interrelationships between the tails of ξ
1 and η. Applications to the asymptotic behavior of the finite-time ruin probability ψ(x,t) in a compound renewal risk model, earlier introduced by Tang et al. (Stat Probab Lett 52, 91–100 (2001)), are given. The asymptotic relations, as initial capital x increases, hold uniformly for t in a corresponding region. These asymptotic results are illustrated in several examples.
相似文献
6.
This paper is a further investigation into the ruin probability ψ(x) in several risk models, where x is the initial surplus. Under the assumption that the claim sizes are heavy‐tailed, we get some tail equivalence relationships of ψ(x). Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
7.
Li Wei 《中国科学A辑(英文版)》2009,52(7):1539-1545
The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this
paper. For claim sizes with common distribution of extended regular variation, we study the asymptotic behaviour of the ruin
probability. As a corollary, we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like
claims.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10571167, 70501028), the Beijing Sustentation
Fund for Elitist (Grant No. 20071D1600800421), the National Social Science Foundation of China (Grant No. 05&ZD008) and the
Research Grant of Renmin University of China (Grant No. 08XNA001) 相似文献
8.
复合Poisson-Geometric风险模型Gerber-Shiu折现惩罚函数 总被引:11,自引:0,他引:11
本文研究赔付为复合Poisson-Geometric过程的风险模型,首先得到了Gerber-Shiu折现惩罚期望函数所满足的更新方程,然后在此基础上推导出了破产概率和破产即刻前赢余分布等所满足的更新方程,再运用Laplace方法得出了破产概率的Pollazek-Khinchin公式,最后根据Pollazek-Khinchin公式,直接得出了当索赔分布服从指数分布的情形下破产概率的显示表达式. 相似文献
9.
The compound binomial risk model with time-correlated claims 总被引:1,自引:0,他引:1
Yuntao Xiao 《Insurance: Mathematics and Economics》2007,41(1):124-133
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
10.
本文研究经典风险模型中破产概率的渐近行为.利用几何和的方法,获得了索赔额的分布属于S(γ).γ〉0。时破产概率的一个局部渐近式.同时.给出了一个具体的数值的例子. 相似文献
11.
In this paper we investigate the ruin probability in a general risk model driven by a compound Poisson process. We derive a formula for the ruin probability from which the Albrecher–Hipp tax identity follows as a corollary. Then we study, as an important special case, the classical risk model with a constant force of interest and loss-carried-forward tax payments. For this case we derive an exact formula for the ruin probability when the claims are exponential and an explicit asymptotic formula when the claims are subexponential. 相似文献
12.
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
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15.
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
16.
Yang Yang Wang Xinzhi Chen Shaoying 《Methodology and Computing in Applied Probability》2022,24(2):1221-1236
Consider a compound renewal risk model, in which a single accident may cause more than one claim. Under the condition that the common distribution of the individual claims is second order subexponential, we establish a second order asymptotic formula for the infinite-time ruin probability. Compared with the traditional ones, our second order asymptotic result is more precise and effective, which can be demonstrated by the numerical studies.
相似文献17.
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This paper is concerned with the numerical computation of the probability ψ(u) of ruin with initial reserve u. The basic assumption states that the claim size distribution is phase-type in the sense of Neuts. The models considered are: the classical compound Poisson risk process, the Sparre Anderse process and varying environments which are either governed by a Markov process or exhibit periodic fluctuations. The computational steps involve the iterative solution of a non-linear matrix equation Q = Ψ (Q) as well as the evaluation of matrix-exponentials eQu. A number of worked-out numerical examples are presented. 相似文献
20.
TaoJiang Chen-mingXu 《应用数学学报(英文版)》2004,20(2):353-356
Subject to the assumption that the common distribution of claim sizes belongs to the extendedregular variation class,the present work obtains a simple asymptotic formula for the ruin probability within arandom or nonrandom horizon in the renewal model. 相似文献