广义双二项风险模型的破产概率和Lundberg不等式

本文将双二项分布风险模型推广到资金利率和通货膨胀率下带干扰的新模型--广义双二项风险模型.然后讨论了盈余过程的性质并利用盈余过程的性质获得了广义双二项风险模型的破产概率和Lundberg不等式,最后就保费额服从混合指数分布的情况进行了分析.     

两类索赔相关风险模型的罚金折现期望函数

考虑两类索赔相关风险模型.两类索赔计数过程分别为独立的广义Poisson过程和广义Erlang(2)过程.得到了该风险模型的罚金折现期望函数满足的积分微分方程及该函数的Laplace变换的表达式,且当索赔额均服从指数分布时,给出了罚金折现期望函数及破产概率的明确表达式.     

上证指数收益率的极值研究

在极值理论广义极值分布模型的基础上,对上证指数日回报率的极值作了实证研究.给出了近两年间出现的极值的概率与等待时间,为风险的度量提供了量化的依据.     

具有两类索赔相关风险过程的罚金折现函数

考虑两类索赔相关风险过程.两类索赔计数过程分别为独立的Poisson和广义Erlang(2)过程.将该过程转换为两类独立索赔风险过程,得到了该过程的罚金折现函数满足的积分微分方程及该函数的拉普拉斯变换的表达式,且当索赔额服从指数分布时,给出了罚金折现函数及破产概率的表达式.     

基于广义CoES方法的金融业与房地产业风险溢出研究

为了克服广义CoVaR只能衡量单一尾部概率下条件风险的局限性,本文提出一种新的风险溢出测度——广义CoES方法,并基于Archimedean Copula函数给出了广义CoES的计算公式。利用该方法对我国金融业与房地产业风险溢出研究的实证结果表明:广义CoVaR相比于广义CoES低估了金融业与房地产业自身的条件风险;两个行业之间存在动态的、非对称的双向风险溢出,房地产业对金融业的平均风险溢出强度为69.71%,而金融业对房地产业的平均风险溢出强度为65.38%;房地产业对金融业的净风险溢出呈现出顺周期性,即当房地产价格低迷时净风险溢出程度较弱,而当房地产价格走高时净风险溢出程度也随之增强。     

一类具有随机保费风险模型的破产问题

本文考虑了一个保费收入过程为复合Poisson过程,且索赔时间间隔分布为广义Erlang(n)分布的风险模型,给出了其罚金折现期望函数所满足的瑕疵更新方程以及渐近表达式和精确表达式.     

常利率下自回归索赔模型的破产概率的界

研究常利率下的一个广义连续时间更新风险模型的(最终)破产概率,其中自回归过程模拟相依的索赔过程.通过更新的递推方法,得到了此模型破产概率的指数上、下界.     

一类相依双险种风险模型的罚金折现期望函数

考虑索赔到达具有相依性的一类双险种风险模型,其中第一类险种的索赔计数过程为Poisson过程,第二类险种的索赔计数过程为其p-稀疏过程与广义Erlang(2)过程的和,利用更新论证得到了此风险模型的罚金折现期望函数满足的微积分方程及其Laplace变换的表达式.并就索赔额均服从指数分布的情形,给出了罚金函数及破产概率的精确表达式.     

带干扰的复合广义齐次Poisson过程的多险种破产概率

将复合广义齐次poisson过程的多险种风险模型推广到带干扰的一种新模型,运用鞅方法破产概率满足的Lundberg不等式和一般公式.     

带扰动的两类索赔风险模型的罚金折扣函数

考虑带扰动的两类索赔风险模型.两类索赔来到的计数过程分别为独立的Poisson过程和广义Erlang(n)过程.得到了此模型的罚金折扣函数的拉普拉斯变换,并且当两类索赔额分布密度的拉普拉斯变换均为有理函数时,给出了罚金折扣函数的具体表达式.     

Discrete–time nonlinear filtering with marked point process observations: ii. risk–sensitive filters

We discuss in this article the risk–sensitive filtering problem of estimating a nonlinear signal process, with nonadditive non–Gaussian noise, via a marked point process observation. This extends to the risk sensitive case all the risk–neutral results studied in Dufour and Kannan [2].By going into a change of measure, we derive the unnormalized conditional density of the signal conditioned on the observation history. We also derive the unnormalized prediction density. Using these, we present two separate expressions for the optimal estimate of the signal. A similar analysis of the smoothing density of the signal is also studied under both the risk–sensitive and risk–neutral cases. We specialize the above optimal estimation to the linear signal dynamics and marked point process observation under some Gaussian assumptions. We obtain a Kalman type risk-sensitive filter. Due to the special nature of the observation process, the conditional mean and covariance estimates directly depend now on the point process     

Statistical estimation for some dividend problems under the compound Poisson risk model

In this paper, we consider some dividend problems in the classical compound Poisson risk model under a constant barrier dividend strategy. Suppose that the Poisson intensity for the claim number process and the distribution for the individual claim sizes are both unknown. We use the COS method to study the statistical estimation for the expected present value of dividend payments before ruin and the expected discounted penalty function. The convergence rates under large sample setting are derived. Some simulation results are also given to show effectiveness of the estimators under finite sample setting.     

Estimations and asymptotic behaviors of coherent entropic risk measure for sums of random variables

In this article, we provide an estimation and several asymptotic behaviors for the coherent entropic risk measure of compound Poisson process. We also establish an estimation for the coherent entropic risk measure of sum of i.i.d. random variables in virtue of Log-Sobolev inequality. As an application, we provide two deviation estimations of the tail probability for compound Poisson process. Finally, several simulation results are given to support our results.     

On estimation in multivariate linear calibration with elliptical errors

The estimation problem in multivariate linear calibration with elliptical errors is considered under a loss function which can be derived from the Kullback-Leibler distance. First, we discuss the problem under normal errors and give unbiased estimate of risk of an alternative estimator by means of the Stein and Stein-Haff identities for multivariate normal distribution. From the unbiased estimate of risk, it is shown that a shrinkage estimator improves on the classical estimator under the loss function. Furthermore, from the extended Stein and Stein-Haff identities for our elliptically contoured distribution, the above result under normal errors is extended to the estimation problem under elliptical errors. We show that the shrinkage estimator obtained under normal models is better than the classical estimator under elliptical errors with the above loss function and hence we establish the robustness of the above shrinkage estimator.     

跳扩散结构下风险最小化动态套期保值策略研究

在标的资产价格服从跳-扩散过程情况下,研究了风险最小化动态套期保值问题.首先用MCMC方法估计得到模型参数值,克服了传统的直接用样本均值和样本方差进行参数估计值的不足,与市场实际更吻合;然后在风险最小目标下,采用逐步倒推法得到随时间改变的动态最优套期保值策略解析表达式,由此可以及时做出策略调整,达到既对冲风险又节约成本的目的.文章最后通过对比分析不同期限、不同策略调整频率情况下的费用投入,得出期限和策略调整频率之间的关系,为套期保值者根据不同情况做出合理的套保策略提供了参考,另外,为满足金融机构进行压力测试或投资者为适应费率调整的需要,也分析说明了不同交易费率和策略之间的关系.     

VaR测度下的风险对冲策略研究

本文分别在正态分布和任意分布设定下讨论最小在险价值(VaR)的风险对冲问题。在正态分布设定下,本文深入讨论最小方差对冲比率和最小VaR对冲比率的性质,并得出最小VaR对冲策略下组合收益率的均值和方差大于最小方差策略下组合收益率的均值和方差。在任意分布设定下,本文构建一种新的VaR对冲模型,该模型引入非参数核估计方法对VaR进行估计,然后基于VaR核估计量建立风险对冲问题,实现风险估计与风险对冲同步进行。实证结果非常稳健地表明,不做任何分布假设下的核估计法得到的风险对冲效果优于最小方差对冲策略和正态分布设定下的最小VaR对冲策略。     

Life expectancy under random censorship

This paper deals with estimation of life expectancy used in survival analysis and competing risk study under the condition that the data are randomly censored by K independent censoring variables. The estimator constructed is based on a theorem due to Berman [2], and it involves an empirical distribution function which is related to the Kaplan-Meier estimate used in biometry. It is shown that the estimator, considered as a function of age, converges weakly to a Gaussian process. It is found that for the estimator to have finite limiting variance requires the assumption that the censoring variables be stochastically larger than the “survival” random variable under investigation.     

一类聚合风险模型

本文提出了一类聚合风险模型--INARCR.研究了相关结构及性质;给出了总理赔量的极小值及拐点的条件和聚合风险模型的中心极限;余额过程中调节系数的系列性质.最后给出了周期d=2时聚合风险模型参数的矩估计.     

A comparison of statistical methods for prenatal screening for Down syndrome

Currently, prenatal screening for Down Syndrome (DS) uses the mother's age as well as three biochemical markers for risk prediction. Risk calculations for the biochemical markers use a quadratic discriminant function. In this paper we compare several classification procedures to quadratic discrimination methods for biochemical-based DS risk prediction, based on data from a prospective multicentre prenatal screening study. We investigate alternative methods including linear discriminant methods, logistic regression methods, neural network methods, and classification and regression-tree methods. Several experiments are performed, and in each experiment resampling methods are used to create training and testing data sets. The procedures on the test data set are summarized by the area under their receiver operating characteristic curves. In each experiment this process is repeated 500 times and then the classification procedures are compared. We find that several methods are superior to the currently used quadratic discriminant method for risk estimation for these data. The implications of these results for prenatal screening programs are discussed.     

二项抽样下基于鞍点逼近方法的流行病相对风险置信区间构造

相对风险是流行病学研究中的重要指标之一,它是度量一种暴露因素是否与某病的致病有联系的统计指标.以该指标的数值大小来表明这一暴露因素对某病的发生具有何种影响及影响的大小,体现了暴露与疾病的关联程度.精确地得到相对风险指标的区间估计,对病因推断具有重要意义.但是由于相对风险指标的估计量是两个概率值的估计量的比值,要得到其精确分布一般而言是很困难的,因此已有研究成果大都采用渐近方法估计相对风险的置信区间,这在小样本情况下表现不佳.在二项抽样条件下,对相对风险的点估计、置信区间估计一直被人们所关注.在二项采样下利用鞍点逼近的方法构造相对风险的置信区间,并通过实例与蒙特卡洛模拟,与传统的置信区间构造方法对比,模拟结果显示其优点,尤其是在小样本量条件下估计效果比较好.