共查询到20条相似文献,搜索用时 31 毫秒
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Jiangyan Peng 《Stochastics An International Journal of Probability and Stochastic Processes》2018,90(3):432-471
In this paper, an insurer is allowed to make risk-free and risky investments, and the price process of the investment portfolio is described as an exponential Lévy process. We study the asymptotic tail behavior for a non-standard renewal risk model with dependence structures. The claim sizes are assumed to follow a one-sided linear process with independent and identically distributed step sizes, and the step sizes and inter-arrival times form a sequence of independent and identically distributed random pairs with a dependence structure. When the step-size distribution is heavy tailed, we obtain some uniform asymptotics for the finite-and infinite-time ruin probabilities. 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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《Insurance: Mathematics and Economics》2013,53(1):206-215
Assuming that the claim sizes of an insurance company have a common distribution with gamma-like tail, we study the asymptotic tail behaviour of the reinsured amounts under the ECOMOR and LCR reinsurance treaties, respectively. Our novel results include a precise asymptotic expansion for the tail probability of the reinsured amounts under the ECOMOR treaty and tight asymptotic bounds for the LCR case. As a by-product we derive a precise asymptotic expansion for the tail of the product of independent regularly varying random variables. 相似文献
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《Insurance: Mathematics and Economics》2002,31(2):205-214
In this paper we consider a risk model with two dependent classes of insurance business. In this model the two claim number processes are correlated. Claim occurrences of both classes relate to Poisson and Erlang processes. We derive explicit expressions for the ultimate survival probabilities under the assumed model when the claim sizes are exponentially distributed. We also examine the asymptotic property of the ruin probability for this special risk process with general claim size distributions. 相似文献
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A uniform asymptotic estimate for discounted aggregate claims with subexponential tails 总被引:2,自引:1,他引:1
In this paper we study the tail probability of discounted aggregate claims in a continuous-time renewal model. For the case that the common claim-size distribution is subexponential, we obtain an asymptotic formula, which holds uniformly for all time horizons within a finite interval. Then, with some additional mild assumptions on the distributions of the claim sizes and inter-arrival times, we further prove that this formula holds uniformly for all time horizons. In this way, we significantly extend a recent result of Tang [Tang, Q., 2007. Heavy tails of discounted aggregate claims in the continuous-time renewal model. J. Appl. Probab. 44 (2), 285–294]. 相似文献
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In this paper, we obtain the asymptotics for the tail probability of the total claim amount with negatively dependent claim
sizes in two cases: in the first case, the distribution tail of the claim number is dominatedly varying; in the second case,
the distribution of the claim number is in the maximum domain of attraction of the Gumbel distribution, and the claim sizes
are light-tailed. In both cases, we assume that the claim sizes are nondegenerate negatively dependent and identically distributed
random variables and that the claim number is not necessarily independent of the claim sizes. As applications, we derive asymptotics
for the finite-time ruin probabilities in some dependent compound renewal risk models with constant interest rate. 相似文献
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The Asymptotic Estimate of Absolute Ruin Probabilities in the Renewal Risk Model with Constant Force of Interest 下载免费PDF全文
In this paper, absolute ruin problems
for a kind of renewal risk model with constant interest force are
studied. For certain situations of the claim distribution with heavy
tail, consider the surplus of the arrival time, and discrete the
surplus process, then use the method of renewal function and
convolution, we present the asymptotic properties of absolute ruin
probability when the initial surplus tends to infinity. 相似文献
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Yang Chen Yang Yang Tao Jiang 《Journal of Mathematical Analysis and Applications》2019,469(2):525-536
Consider a continuous-time bidimensional risk model with constant force of interest in which the claim sizes from the same business are heavy-tailed and upper tail asymptotically independent. We investigate two cases: one is that the two claim-number processes are arbitrarily dependent, and the other is that the two corresponding claim inter-arrival times from different lines are positively quadrant dependent. Some uniformly asymptotic formulas for finite-time ruin probability are established. 相似文献
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Danijel Grahovac 《Methodology and Computing in Applied Probability》2018,20(1):273-288
In this paper, we consider the classical yet widely applicable Cramér-Lundberg risk model with Pareto distributed claim sizes. Building on the previously known expression for the ruin probability we derive distributions of different ruin-related quantities. The results rely on the theory of scale functions and are intended to illustrate the simplicity and effectiveness of the theory. A particular emphasis is put on the tail behavior of the distributions of ruin-related quantities and their tail index value is established. Numerical illustrations are provided to show the influence of the claim sizes distribution tail index on the tails of the ruin-related quantities distribution. 相似文献
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We generalize an integral representation for the ruin probability in a Crámer-Lundberg risk model with shifted (or also called US-)Pareto claim sizes, obtained by Ramsay (2003), to classical Pareto(a) claim size distributions with arbitrary real values a>1 and derive its asymptotic expansion. Furthermore an integral representation for the tail of compound sums of Pareto-distributed claims is obtained and numerical illustrations of its performance in comparison to other aggregate claim approximations are provided. 相似文献
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This paper investigates the ruin probabilities of a renewal risk model with stochastic investment returns and dependent claim sizes. The investment is described as a portfolio of one risk‐free asset and one risky asset whose price process is an exponential Lévy process. The claim sizes are assumed to follow a one‐sided linear process with independent and identically distributed step sizes. When the step‐size distribution is heavy tailed, we establish some uniform asymptotic estimates for the ruin probabilities of this renewal risk model. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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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
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M.S. Bratiychuk 《Insurance: Mathematics and Economics》2007,41(1):156-162
In this paper, we present the classical risk process with two-step premium function. This means that the gross risk premium rate changes if the insurer’s surplus reaches a certain threshold level. The formula for the infinite-time ruin probability is obtained. The asymptotic behaviour of the ruin probability in the case where the claim size distribution has a light tail is considered as well. 相似文献
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Asymptotic behaviour of the finite-time ruin probability under subexponential claim sizes 总被引:3,自引:0,他引:3
The paper deals with the Sparre Andersen risk model. We study the tail behaviour of the finite-time ruin probability, Ψ(x,t), in the case of subexponential claim sizes as initial risk reserve x tends to infinity. The asymptotic formula holds uniformly for t in a corresponding region and reestablishes a formula of Tang [Tang, Q., 2004a. Asymptotics for the finite time ruin probability in the renewal model with consistent variation. Stochastic Models 20, 281–297] obtained for the class of claim distributions having consistent variation. 相似文献
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Jinzhu Li 《Journal of Mathematical Analysis and Applications》2012,387(2):1009-1023
In this paper we study the asymptotic tail behavior for a non-standard renewal risk model with a dependence structure and stochastic return. An insurance company is allowed to invest in financial assets such as risk-free bonds and risky stocks, and the price process of its portfolio is described by a geometric Lévy process. By restricting the claim-size distribution to the class of extended regular variation (ERV) and imposing a constraint on the Lévy process in terms of its Laplace exponent, we obtain for the tail probability of the stochastic present value of aggregate claims a precise asymptotic formula, which holds uniformly for all time horizons. We further prove that the corresponding ruin probability also satisfies the same asymptotic formula. 相似文献
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A local limit theorem for the probability of ruin 总被引:4,自引:0,他引:4
YIN ChuancunDepartment of Mathematics Qufu Normal University Qufu China 《中国科学A辑(英文版)》2004,47(5):711-721
In this paper, we give a result on the local asymptotic behaviour of the probability of ruin in a continuous-time risk model in which the inter-claim times have an Erlang distribution and the individual claim sizes have a distribution that belongs to S(v) with v≥ 0, but where the Lundberg exponent of the underlying risk process does not exist. 相似文献
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《高校应用数学学报(英文版)》2015,(3)
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