基于极值分布理论的WVaR度量研究及实证分析

本文研究了基于极值分布理论的WVaR度量方法在金融风险度量中的应用.采用广义Pareto模型的WVaR方法,对上证综合指数、深证成分指数、标准普尔指数、纳斯达克指数进行了风险度量研究.实证分析结果表明,对比于其他没有考虑投资者风险偏好的度量方法,含有投资者风险偏好的WVaR更能准确地度量金融市场的风险情况.在同一市场环境下,风险值相差不大,存在共动性,国内新兴市场风险值比国外相对发达稳定市场的风险值要大.     

混合双参数广义Pareto分布的参数估计

Pareto分布族因其厚尾特点,在金融分析、寿命分析中都是非常重要的统计模型.但是对于混合双参广义Pareto分布,在模型参数估计时,传统的矩法估计和极大似然估计在理论上可以实现,实践时比较困难.本文应用EM算法之ECM算法,研究了混合广义Pareto分布在完全数据场合下的参数估计问题,并模拟说明EM算法来估计混合广义Pareto分布是一种容易实现又非常有效的方法.     

不确定下广义博弈强Berge均衡的存在性

本文基于不确定下的非合作博弈NS均衡给出了不确定下广义非合作博弈强Berge均衡与广义多目标弱Pareto强Berge均衡的定义,利用Fan-Glicksberg不动点定理证明了不确定下广义非合作博弈强Berge均衡与不确定下广义多目标弱Pareto强Berge均衡存在性定理.     

Gamma分布与其它分布的若干定理

利用条件概率的性质,得到Gamma分布与Poisson分布、广义负二项分布、广义Pareto分布的若干定理及推论.     

基于MGPD模型的地质灾害风险的统计度量

利用扩展BurrⅫ分布构建了改进的广义帕累托分布模型—MGPD模型(Meliorated Generalized Pareto Distribution),由此得到了地质灾害损失的在险风险值和最大可能损失估计值。以湖南省娄底市地质灾害损失数据实证分析,结果显示:MGPD模型在刻画地质灾害损失数据时,比GPD模型的精度更高,具有更广泛的适用性。     

基于POT模型的巨灾风险度量与保险模式研究——以地震风险为例

巨灾风险发生的频率低且损失大,具有显著的厚尾性特征,因此不易度量其风险。本文以地震风险为例,采用1961-2011年以来中国发生的4.5级以上地震造成的损失值作为样本,在进行物价调整之后引入了POT模型和广义Pareto分布对损失数据进行拟合,计算出不同的置信度水平下不同的VaR值,得到不同的保费规模与地震保险的价格,并以此为依据设计我国巨灾保险的风险分散机制。     

广义Pareto分布参数的经验Bayes估计的收敛速度

在加权平方损失函数下,获得广义Pareto分布形状参数的经验Bayes(EB)估计,并得到了该估计的收敛速度.     

金融市场极端日收益数据的广义Pareto分布拟合

本文基于极值理论和方法建立了上证综合指数极端日收益率的广义Pareto模型,并利用所得的模型计算出日收益率的返回水平及其上尾概率。将估计的日收益率模型比较得出,在实施涨跌停板前,日收益率的上尾明显厚于实施涨跌停板后的上尾,说明了实施该制度可以有效的控制股票市场的投机现象,从而降低投资者的收益损失风险。     

车辆荷载作用下桥梁应变极值估计的阈值选取

采用过阈法估计车辆荷载作用下桥梁的应变极值,合理的阈值选取十分关键.阈值选取过大,信息量少,阈值选取过小,广义Pareto分布模型参数估计偏差大.常用的阈值选取方法不能较好地适用于车辆荷载作用下的应变极值估计.基于太平湖大桥车辆荷载作用下1年的应变数据,对拟合结果较好的3种混合分布进行Monte-Carlo(蒙特 卡洛)抽样,对比同一样本基于不同阈值的广义Pareto分布模型的极值估计结果,提出了一种经验式的阈值选取方法.与常用阈值选取方法相比,根据文中方法所得阈值估计的周应变极值分布与实测结果更为接近,估计结果更好.     

Pareto严格稳定分布在保险理赔中的应用

本文研究了Pareto严格稳定分布在保险中的应用.利用极大似然估计的方法得到了Pareto严格稳定分布,正态分布和Pareto分布的参数估计.根据信息准则,表明Pareto严格稳定分布能够较好地拟合保险数据.     

Modelling lifetime dependence for older ages using a multivariate Pareto distribution

The main driver of longevity risk is uncertainty in old-age mortality, especially surrounding potential dependence structures. We investigate a multivariate Pareto distribution that allows for the exploration of a variety of applications, from portfolios of standard annuities to joint-life annuity products for couples. Given the anticipated continued increase of supercentenarians, the heavy-tailed nature of the Pareto distribution is appropriate for this application. In past work, it has been shown that even a little dependence between lives can lead to much higher uncertainty. Therefore, the ability to assess and incorporate the appropriate dependence structure, whilst allowing for extreme observations, significantly improves the pricing and risk management of life-benefit products.     

Comparing extreme models when the sign of the extreme value index is known

In the literature on analyzing extremes, both generalized Pareto distributions and Pareto distributions are employed to infer the tail of a distribution with a known positive extreme value index. Similar studies exist for a known negative extreme value index. Intuitively, one should not employ the generalized Pareto distribution in the case of knowing the sign of the extreme value index. In this work, we show that fitting a generalized Pareto distribution is equivalent to the model in Hall (1982) in the case of a negative extreme value index, in both improving the rate of convergence and including the bias term of the asymptotic results of that reference. When the extreme value index is known to be positive, we show that fitting a generalized Pareto distribution may be preferred in some cases determined by a so-called second-order parameter and the extreme value index itself.     

沪深股市收益分布尾部特征研究

本文运用跳跃扩散模型和极值理论方法对沪深股指收益分布特征进行了研究。跳跃扩散模型定量化地给出沪深股市股票收益分布产生的原因,沪深股市收益分布为具有胖尾的非正态分布,股票收益变动主要是由离散信息作用引起,一般帕累托分布较好地拟合股票收益左尾分布。     

Robust Estimation of the Generalized Pareto Distribution

One approach used for analyzing extremes is to fit the excesses over a high threshold by a generalized Pareto distribution. For the estimation of the shape and scale parameters in the generalized Pareto distribution, under some restrictions on the value of the scale parameter, maximum likelihood, method of moments and probability weighted moments' estimators are available. However, these are not robust estimators. In this paper we implement a robust estimation procedure known as the method of medians (He and Fung, 1999) to estimate the parameters in the generalized Pareto distribution. The asymptotic distribution of our estimator is normal for any value of the shape parameter except –1.     

Tail Conditional Expectation for the Multivariate Pareto Distribution of the Second Kind: Another Approach

In risk analysis, the Tail Conditional Expectation (TCE) describes the expected amount of risk that can be experienced given that the risk exceeds a threshold value. Thus, TCE provides an important measure of the right-tail risk. In this paper, we present TCE formulas for the multivariate Pareto distribution of the second kind. Because of the complex form of this distribution, the formulas for the n-variate case are expressed recursively, in terms of the (n ? 1)-variate case.     

Modelling losses and locating the tail with the Pareto Positive Stable distribution

This paper focuses on modelling the severity distribution. We directly model the small, moderate and large losses with the Pareto Positive Stable (PPS) distribution and thus it is not necessary to fix a threshold for the tail behaviour. Estimation with the method of moments is straightforward. Properties, graphical tests and expressions for value-at risk and tail value-at-risk are presented. Furthermore, we show that the PPS distribution can be used to construct a statistical test for the Pareto distribution and to determine the threshold for the Pareto shape if required. An application to loss data is presented. We conclude that the PPS distribution can perform better than commonly used distributions when modelling a single loss distribution for moderate and large losses. This approach avoids the pitfalls of cut-off selection and it is very simple to implement for quantitative risk analysis.     

Modelling losses and locating the tail with the Pareto Positive Stable distribution

This paper focuses on modelling the severity distribution. We directly model the small, moderate and large losses with the Pareto Positive Stable (PPS) distribution and thus it is not necessary to fix a threshold for the tail behaviour. Estimation with the method of moments is straightforward. Properties, graphical tests and expressions for value-at risk and tail value-at-risk are presented. Furthermore, we show that the PPS distribution can be used to construct a statistical test for the Pareto distribution and to determine the threshold for the Pareto shape if required. An application to loss data is presented. We conclude that the PPS distribution can perform better than commonly used distributions when modelling a single loss distribution for moderate and large losses. This approach avoids the pitfalls of cut-off selection and it is very simple to implement for quantitative risk analysis.     

单参数Pareto分布变点估计研究

研究单参数Pareto分布存在变点时的估计问题,分别利用极大似然估计法和贝叶斯方法对单参数Pareto分布的变点进行估计,并运用Matlab软件进行随机模拟,随机结果表明贝叶斯方法与极大似然估计相比,估计值更接近真值.     

Pareto分布中门槛值的确定及其在股票市场中的应用

本文根据Pareto分布与两参数指数分布之间的相互关系,利用两参数指数分布的拟合优度检验统计量给出了确定Pareto分布的门槛值的一种方法。利用道琼斯指数和上证综合指数的收益率序列说明所给方法,结果表明所给方法优于现有方法。     

Risk aggregation in multivariate dependent Pareto distributions

In this paper we obtain closed expressions for the probability distribution function of aggregated risks with multivariate dependent Pareto distributions. We work with the dependent multivariate Pareto type II proposed by Arnold (1983, 2015), which is widely used in insurance and risk analysis. We begin with an individual risk model, where the probability density function corresponds to a second kind beta distribution, obtaining the VaR, TVaR and several other tail risk measures. Then, we consider a collective risk model based on dependence, where several general properties are studied. We study in detail some relevant collective models with Poisson, negative binomial and logarithmic distributions as primary distributions. In the collective Pareto–Poisson model, the probability density function is a function of the Kummer confluent hypergeometric function, and the density of the Pareto–negative binomial is a function of the Gauss hypergeometric function. Using data based on one-year vehicle insurance policies taken out in 2004–2005 (Jong and Heller, 2008) we conclude that our collective dependent models outperform other collective models considered in the actuarial literature in terms of AIC and CAIC statistics.