Empirical bounds for ruin probabilities

We consider the classical model for an insurance business where the claims occur according to a Poisson process and where the distribution for the cost of each claim fulfills Cramér's tail-condition. Under these conditions Lundberg's constant R is of fundamental importance for ruin calculations.We derive estimates of R, based on an observation of the insurance business and investigate the statistical properties of those estimates. We further derive bounds and confidence intervals for ruin probabilities.     

船舶碰撞危险度模型的构建

运用模糊数学的综合评判理论,把会遇中目标船的DCPA、TCPA两船距离、相对方位、船速比5个因素作为基本评判参数,建立碰撞危险度的评价模型．而将其它因素,如航行区域状况、能见度情况和船舶的操纵性能等,作为对上述因素的危险隶属度函数的修正加以考虑．引入了船舶领域、动界等概念,以对来船构成的本船危险度进行客观有效地评价,为安全避碰提供合理依据．     

Estimation of the Multivariate Normal Precision Matrix under the Entropy Loss

Let X ₁, , X _n (n > p) be a random sample from multivariate normal distribution N _p (, ), where R ^p and is a positive definite matrix, both and being unknown. We consider the problem of estimating the precision matrix ^–1. In this paper it is shown that for the entropy loss, the best lower-triangular affine equivariant minimax estimator of ^–1 is inadmissible and an improved estimator is explicitly constructed. Note that our improved estimator is obtained from the class of lower-triangular scale equivariant estimators.     

Bayesian networks applied to credit scoring

Email: kchang{at}gmu.eduEmail: RobertFung{at}Fairlsaac.comEmail: alan.lucas{at}hotmail.com^¶Email: BobOliver{at}Fairlsaac.com^||Email: NShikaloff{at}Fairlsaac.com The objectives of this paper are to apply the theory and numericalalgorithms of Bayesian networks to risk scoring, and comparethe results with traditional methods for computing scores andposterior predictions of performance variables. Model identification,inference, and prediction of random variables using Bayesiannetworks have been successfully applied in a number of areas,including medical diagnosis, equipment failure, informationretrieval, rare-event prediction, and pattern recognition. Theability to graphically represent conditional dependencies andindependencies among random variables may also be useful incredit scoring. Although several papers have already appearedin the literature which use graphical models for model identification,as far as we know there have been no explicit experimental resultsthat compare a traditionally computed risk score with predictionsbased on Bayesian learning algorithms. In this paper, we examine a database of credit-card applicantsand attempt to ‘learn’ the graphical structure ofthe characteristics or variables that make up the database.We identify representative Bayesian networks in a developmentsample as well as the associated Markov blankets and cliquestructures within the Markov blanket. Once we obtain the structureof the underlying conditional independencies, we are able toestimate the probabilities of each node conditional on its directpredecessor node(s). We then calculate the posterior probabilitiesand scores of a performance variable for the development sample.Finally, we calculate the receiver operating characteristic(ROC) curves and relative profitability of scorecards basedon these identifications. The results of the different modelsand methods are compared with both development and validationsamples. Finally, we report on a statistical entropy calculationthat measures the degree to which cliques identified in theBayesian network are independent of one another.     

响应面方法计算HTR-10余热排出系统物理过程的失效概率

在核电站安全研究中，概率安全评价方法已经得到了广泛的应用.但是对于采用非能动设计的核电站系统，其可靠性分析的研究还处于初级阶段.非能动系统的失效不但要考虑常规可靠性分析中考虑的设备失效，还要考虑物理过程的失效.物理过程失效概率的计算方法和能动系统可靠性分析方法完全不同.本文给出物理过程失效的数学描述，介绍了一次二阶矩法、响应面方法，并且应用响应面方法计算了清华大学核能技术设计研究院10MW高温气冷实验堆(HTR-10)余热排出系统失效概率的近似值. 关键词： 概率安全评价 非能动系统 可靠性 响应面     

Proficiency testing in occupational and environmental health – Current practice and international initiatives for harmonisation

An increasing number of proficiency testing schemes (PT schemes) related to occupational and environmental health have been organised. Most schemes emphasise the importance of the validation of analytical results. With regards to harmonisation of the schemes, there are many differences between the schemes at many levels. These include factors concerning their relationship with legislation, national status, type and quality of proficiency testing material, analytical range and priorities for future development. Since differences between PT schemes have been recognised at the European level by organisers of PT schemes and external quality assessment schemes (EQASs) it seems appropriate to reinforce collaboration between scheme organisers in order to improve the quality of analytical performance in occupational and environmental health.     

多级模糊综合评判在高校教师考评中的应用

介绍了模糊综合评判的数学模型.并将二级模糊综合评判用于高校教师的考评,为客观地评价教师提供了一种定量的、科学的方法.     

复合二项过程风险模型的精细大偏差及有限时间破产概率

讨论基于客户到来的复合二项过程风险模型.在该风险模型中,假设索赔额序列是独立同分布的重尾随机变量序列,不同保单发生实际索赔的概率可以不同,则在索赔额服从ERV的条件下,得到了损失过程的精细大偏差;进一步地,得到了有限时间破产概率的Lundberg极限结果.     

A note on natural risk statistics

Recently Heyde, Kou and Peng [C.C. Heyde, S.G. Kou, X.H. Peng, What is a good external risk measure: Bridging the gaps between robustness, subadditivity, and insurance risk measures, 2007, preprint.] proposed the notion of a natural risk statistic associated with a finite sample that relaxes the subadditivity assumption in the classical coherent risk statistics. In this note we use convex analysis to provide alternate proofs of the representation results regarding natural risk statistics.