一类过程需求存贮系统的策略研究及其费用弹性分析

本文首先讨论了需求到达为复合泊松随机过程的库存管理问题,给出了在单位时间内期望总成本费用最小的条件下的确定性的最优订货策略(Q,T).然后分析了在订购量和订购周期为随机变量,其联合分布已知的条件下,基于随机局部弹性理论,分析了总费用关于订购量和订购周期的局部弹性的联合分布,为订购策略的制定提供了合理的依据.     

汽车交通事故损失分布的尾部估计

由于巨额损失对保险公司的影响非常大,费率厘定过程中对极值分布的研究非常重视。本文从极值理论的角度出发,以上海市虹口区2003年的汽车交通事故损失数据为样本,探讨了损失分布的尾部估计方法,并利用该地区2006年的汽车交通事故损失对结论进行了验证。研究结果发现,广义帕雷托分布确实对损失额的尾部提供了较好的拟合,但这依赖于门槛值的恰当选择。传统的门槛值选择方法主观性较强,而通过重复多次的交叉验证技巧,我们可以估计广义帕雷托分布的最合适门槛值位置。     

与两个更新过程有关的某些联合分布

本文讨论的两个时偶问题涉及来一个泊松过程与一个更新过程穿越时间和更新数的联合分布．利用向量马氏过程方法得到了这些联合分布的变换，给出了一个与分布均值有关量的数值结果．     

一类索赔相关风险模型破产概率的研究

本文讨论一类索赔相关同时保费收取为一复合泊松过程的风险模型的破产问题，给出相应的Lundberg不等式．     

失真风险保费的最优经验厘定

研究了贝叶斯模型中失真风险保费的经验厘定问题.通过引入分布函数的加权积分损失函数,利用信度理论的方法最小化期望损失得到分布函数的最优线性估计,进而得到失真风险保费的两个信度估计,并对信度估计的统计性质进行了比较.文章还讨论了失真函数和权重函数的选取问题,给出了结构参数的估计方法,证明了估计的无偏性和相合性.最后,利用数值模拟的方法验证了估计的收敛情况,并对不同失真函数下的收敛情况进行了比较.     

基于贝叶斯分析的中国商业银行内部欺诈分析

内部欺诈事件类型是中国商业银行最严重的操作风险类型。但由于操作风险本质特征和中国商业银行内部欺诈损失数据收集年度较短,数据匮乏,小样本数据容易导致参数结果不稳定。为了在小样本数据下进行更准确的度量,本文采用贝叶斯马尔科夫蒙特卡洛模拟方法,在损失分布法框架下,假设损失频率服从泊松-伽马分布,而损失强度服从广义帕累托-混合伽马分布,分析后验分布的形式,获得中国商业银行不同业务线的内部欺诈损失频率和损失强度的后验分布估计,并进行蒙特卡罗模拟获得不同业务线内部欺诈的风险联合分布。结果表明,拟合结果很好,与传统极值分析法相比,基于利用贝叶斯的分析获得的后验分布可以作为未来的先验分布,有利于在较小样本下获得较真实的参数估计,本方法有助于银行降低监管资本要求。     

一类带干扰索赔相关风险模型的破产概率

讨论一类带干扰索赔相关且保费收取为一复合泊松过程风险模型的破产问题，利用鞅方法得出Lundberg不等式和最终破产概率公式。     

基于离散枢轴量的泊松分布参数的精确最短置信区间

将泊松分布参数的充分统计量的离散型分布函数转化为生存伽马分布函数,以此为枢轴量构造了泊松分布参数的精确置信区间.通过数值模拟,选择合适的置信度组合,得到精确最短置信区间.讨论了大样本下泊松分布参数的近似置信区间的估计精度,验证了精确最短置信区间的计算结果.     

带干扰复合泊松模型下对调整系数的新研究(英文)

本文研究了带干扰复合泊松模型中采用成数再保与超额损失再保险混合策略时作为自留额水平函数的调整系数.我们按照原始条款计算成数再保费,按照期望值保费原则计算超额损失再保费,这样得到了调整系数是超额损失自留额极限的单峰函数的结论.本文最后部分给出了有限时间破产概率的上界.     

复合泊松过程的可加性

对复合泊松分布可加性的研究在许多的文献中都可以看到,本文首先应用特征函数的方法证明了复合泊松分布的可加性.以此为基础,结合对随机过程相关性质的讨论,证明了复合泊松过程也具有与复合泊松分布可加性相似的,某种意义上的可加性性质.     

二元极值分布混合模型的矩估计

极值理论在各个领域得到了越来越多的关注和应用, 尤其是多元极值分布. 而矩估计是一种经典的参数估计方法, 计算简单且具有某些优良性, 本文给出边缘为标准指数分布的二元极值混合模型相关参数的矩估计及其渐近方差. 并将其与极大似然估计的渐近方差比较, 结果表明矩估计是一个较好的估计.     

定数截尾下极值分布的参数估计

本文利用极值分布的一些特性和不动点原理,讨论了定数截尾情形下极值分布参数的估计问题,并提出了一种新的迭代算法;模拟结果显示,这种方法收敛速度快,且不受初始值选取的限制.     

Component risk in multiparameter estimation

Summary For estimating the mean of ap-variate normal distribution under a quadratic loss, a class of estimators, known as Stein's estimators, is known to dominate the maximum likelihood estimator (MLE) forp≧3. But, whereas the risk of the MLE has the same value, equal to a constant, for each component, the maximum component risk of Stein's estimator is large for large values ofp. Certain modification of Stein's rule has been proposed in the literature for reducing the maximum component risk. In this paper, a new rule is given for reducing the maximum component risk. The new rule yields larger reduction in the maximum component risk, compared to its competitor.     

二项-广义Pareto复合极值分布模型的统计推断

极值理论主要研究小概率、大影响的极端事件.当前,复合极值分布已经广泛应用于水文、气象、地震、保险、金融等领域.本文以极值类型定理和PBDH定理为理论依据,构建了二项-广义Pareto复合极值分布模型;使用概率加权矩方法,对所建立的复合模型推导参数估计式;利用计算机模拟,得到了Kolmogorov-Smirnov(简称KS)检验统计量的临界值.     

Intensity‐based estimation of extreme loss event probability and value at risk

We develop a methodology for the estimation of extreme loss event probability and the value at risk, which takes into account both the magnitudes and the intensity of the extreme losses. Specifically, the extreme loss magnitudes are modeled with a generalized Pareto distribution, whereas their intensity is captured by an autoregressive conditional duration model, a type of self‐exciting point process. This allows for an explicit interaction between the magnitude of the past losses and the intensity of future extreme losses. The intensity is further used in the estimation of extreme loss event probability. The method is illustrated and backtested on 10 assets and compared with the established and baseline methods. The results show that our method outperforms the baseline methods, competes with an established method, and provides additional insight and interpretation into the prediction of extreme loss event probability. Copyright © 2012 John Wiley & Sons, Ltd.     

A Predictive Approach to Tail Probability Estimation

One of the issues contributing to the success of any extreme value modeling is the choice of the number of upper order statistics used for inference, or equivalently, the selection of an appropriate threshold. In this paper we propose a Bayesian predictive approach to the peaks over threshold method with the purpose of estimating extreme quantiles beyond the range of the data. In the peaks over threshold (POT) method, we assume that the threshold identifies a model with a specified prior probability, from a set of possible models. For each model, the predictive distribution of a future excess over the corresponding threshold is computed, as well as a conditional estimate for the corresponding tail probability. The unconditional tail probability for a given future extreme observation from the unknown distribution is then obtained as an average of the conditional tail estimates with weights given by the posterior probability of each model.     

Moment Estimation for Multivariate Extreme Value Distribution in a Nested Logistic Model

This paper considers multivariate extreme value distribution in a nested logistic model. The dependence structure for this model is discussed. We find a useful transformation that transformed variables possess the mixed independence. Thus, the explicit algebraic formulae for a characteristic function and moments may be given. We use the method of moments to derive estimators of the dependence parameters and investigate the properties of these estimators in large samples via asymptotic theory and in finite samples via computer simulation. We also compare moment estimation with a maximum likelihood estimation in finite sample sizes. The results indicate that moment estimation is good for all practical purposes.     

一种均匀分布的修正分布——UR-n分布

从现实应用中 ,提出一种均匀分布的修正分布 ,并进一步研究了n次修正分布———UR n分布的性质及其极限性质 .这一分布在军事中武器精度的研究、天文观测等多方面都很有利用价值 .     

Dependence between two multivariate extremes

We extend the characterizations given by Takahashi (1988) for the independence and the total dependence of the univariate marginals of a multivariate extreme value distribution to its multivariate marginals. We also deal with the problem of how to measure the strength of the dependence among multivariate extremes. By presenting new definitions for the extremal coefficient, we propose measures that summarize the dependence between two multivariate extreme value distributions and preserve the main properties of the known bivariate coefficient for two univariate extreme value distributions. Finally, we illustrate these contributions to model the dependence among multivariate marginals with examples.