共查询到20条相似文献,搜索用时 218 毫秒
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本文考虑随机加权和及其最大值尾概率的渐近性,其中增量{X_i,i≥1}为一列独立同分布的实值随机变量,权重{θ_i,i≥1}为另一列非负的随机变量,并且两列随机变量满足某种相依结构.在增量的共同分布F属于控制变换分布族的条件下,我们得到了随机加权和及其最大值尾概率的弱渐近等价估计.特别地,当F属于一致变换分布族时,得到了渐近等价估计.最后,我们将该结果应用于破产概率的渐近估计. 相似文献
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考虑具有一般投资收益过程的二维带扰动保险风险模型,假定保险公司盈余的投资收益过程由右连左极随机过程刻画,且两种索赔额与索赔到达时间间隔服从S armanov相依结构.当索赔额分布属于正则变化尾分布族时,得到有限时间破产概率的渐近公式.当描述投资收益过程的右连左极过程分别取Lévy过程,Vasicek利率模型,Cox-Ingersoll-Ross(CIR)利率模型,Heston模型时,得到相应投资收益情形下破产概率的渐近公式. 相似文献
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研究了控制变换尾分布的宽象限相依实值随机变量部分和的中偏差.相应于所得到的理论结果,进一步给出了在相依保险风险模型中的两个应用;一是在基于顾客到达过程的保险风险模型中,保险公司盈余的渐近估计;二是在复合更新风险模型中,有限时和无限时破产概率的一致渐近估计. 相似文献
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《高校应用数学学报(A辑)》2020,(1)
考虑一类复合相依更新风险模型,一次事故引发多次索赔.假设索赔次数与索赔时刻相依,同一事故引起的索赔额是宽上限相依(widely upper orthant dependent)且服从重尾分布.得到该风险模型损失过程的精细大偏差和有限时破产概率的渐近估计. 相似文献
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研究一类具有利率和相依索赔额的离散风险模型.在模型中,索赔额服从具有独立同分布步长的单边线性过程,贴现因子具有关于利率与时间的一般函数形式.在步长服从重尾分布的条件下,得到了最终破产概率的渐近估计.并通过具体实例分析利率对破产概率的影响. 相似文献
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Chengguo Weng Yi Zhang Ken Seng Tan 《Methodology and Computing in Applied Probability》2013,15(3):655-682
This paper considers the tail behavior of Poisson shot noise processes where the shock random variables are generally dependent but bivariate upper tail independent. Some uniform asymptotic relations are established for tail probabilities of the process. As the Poisson shot noise process can capture the effects of delay factors and the interest factor in the insurance business, these established results are very useful in many insurance applications. As examples, they are applied to two important actuarial topics: ruin probabilities and insurance premium approximation. 相似文献
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We study a class of non-stationary shot noise processes which have a general arrival process of noises with non-stationary arrival rate and a general shot shape function. Given the arrival times, the shot noises are conditionally independent and each shot noise has a general (multivariate) cumulative distribution function (c.d.f.) depending on its arrival time. We prove a functional weak law of large numbers and a functional central limit theorem for this new class of non-stationary shot noise processes in an asymptotic regime with a high intensity of shot noises, under some mild regularity conditions on the shot shape function and the conditional (multivariate) c.d.f. We discuss the applications to a simple multiplicative model (which includes a class of non-stationary compound processes and applies to insurance risk theory and physics) and the queueing and work-input processes in an associated non-stationary infinite-server queueing system. To prove the weak convergence, we show new maximal inequalities and a new criterion of existence of a stochastic process in the space given its consistent finite dimensional distributions, which involve a finite set function with the superadditive property. 相似文献
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Yinghui Dong Kam C. Yuen Guojing Wang Chongfeng Wu 《Methodology and Computing in Applied Probability》2016,18(2):459-486
In this paper, we consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes that the intensities of the default times are driven by macro-economy described by a homogenous Markov chain and that the default of one firm may trigger a positive jump, associated with the state of Markov chain, in the default intensity of the other firm. The intensities before the default of the other firm are modeled by a two-dimensional regime-switching shot noise process with common shocks. By using the idea of “change of measure” and some closed-form formulas for the joint conditional Laplace transforms of the regime-switching shot noise processes and the integrated regime-switching shot noise processes, we derive the two-dimensional conditional and unconditional joint distributions of the default times. Based on these results, we can express the single-name credit default swap (CDS) spread, the first and second-to-default CDS spreads on two underlyings in terms of fundamental matrix solutions of linear, matrix-valued, ordinary differential equations. 相似文献
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For a first-order non-explosive autoregressive process with dependent noise, we propose a truncated sequential procedure with
a fixed mean-square accuracy. The asymptotic distribution of the estimator depends on the type of the noise distribution:
it is normal when the noise has a Kotz’s distribution, while it is a mixture of normal distributions if the noise distribution
is a variance mixture of normal distrbutions as well. In both cases, the convergence to the limiting distribution is uniform
in the unknown parameter.
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We consider the asymptotic joint distribution of the eigenvalues and eigenvectors of Wishart matrix when the population eigenvalues become infinitely dispersed. We show that the normalized sample eigenvalues and the relevant elements of the sample eigenvectors are asymptotically all mutually independently distributed. The limiting distributions of the normalized sample eigenvalues are chi-squared distributions with varying degrees of freedom and the distribution of the relevant elements of the eigenvectors is the standard normal distribution. As an application of this result, we investigate tail minimaxity in the estimation of the population covariance matrix of Wishart distribution with respect to Stein's loss function and the quadratic loss function. Under mild regularity conditions, we show that the behavior of a broad class of tail minimax estimators is identical when the sample eigenvalues become infinitely dispersed. 相似文献
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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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Ioannides D.A. Papanastassiou D.P. 《Statistical Inference for Stochastic Processes》2001,4(2):181-198
A nonparametric estimation of a distribution function is considered when observations contain measurement errors. A method
is developed to establish asymptotic normality results for a deconvoluting kernel-type estimator for ρ-mixing stochastic processes
corrupted by some noise process. It is shown that the asymptotic distribution depends on the smoothness of the noise distributions,
which are characterized as either ordinary smooth or super smooth. Also, the kind of dependence of the noise process is crucial
to the form of the asymptotic variance.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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In this study, we investigate the tail probability of the discounted aggregate claim sizes in a dependent risk model. In this model, the claim sizes are observed to follow a one-sided linear process with independent and identically distributed innovations. Investment return is described as a general stochastic process with c`adl`ag paths. In the case of heavy-tailed innovation distributions, we are able to derive some asymptotic estimates for tail probability and to provide some asymptotic upper bounds to improve the applicability of our study. 相似文献
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Victor Konev Serguei Pergamenchtchikov 《Annals of the Institute of Statistical Mathematics》2010,62(6):1083-1111
This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive
stationary Gaussian noise having unknown correlation function. A general model selection procedure on the basis of arbitrary
projective estimates, which does not need the knowledge of the noise correlation function, is proposed. A non-asymptotic upper
bound for L2{\mathcal{L}_2} -risk (oracle inequality) has been derived under mild conditions on the noise. For the Ornstein–Uhlenbeck noise the risk
upper bound is shown to be uniform in the nuisance parameter. In the case of Gaussian white noise the constructed procedure
has some advantages as compared with the procedure based on the least squares estimates (LSE). The asymptotic minimaxity of
the estimates has been proved. The proposed model selection scheme is extended also to the estimation problem based on the
discrete data applicably to the situation when high frequency sampling can not be provided. 相似文献