A Spatial Cross-Sectional Credibility Model with Dependence Among Risks

A Bühlmann-Straub type credibility model with dependence structure among risk parameters and conditional spatial cross-sectional dependence is studied. Predictors of future losses for the model under both types of dependence are derived by minimizing the expected quadratic loss function, and nonparametric estimators of structural parameters are considered in the spatial statistics context. Predictions and estimations made for the proposed model are examined and compared to other models in an application with crop insurance data and in a simulation study.     

Credibility Using Copulas

Abstract

Credibility is a form of insurance pricing that is widely used, particularly in North America. The theory of credibility has been called a “cornerstone” in the field of actuarial science. Students of the North American actuarial bodies also study loss distributions, the process of statistical inference of relating a set of data to a theoretical (loss) distribution. In this work, we develop a direct link between credibility and loss distributions through the notion of a copula, a tool for understanding relationships among multivariate outcomes.

This paper develops credibility using a longitudinal data framework. In a longitudinal data framework, one might encounter data from a cross section of risk classes (towns) with a history of insurance claims available for each risk class. For the marginal claims distributions, we use generalized linear models, an extension of linear regression that also encompasses Weibull and Gamma regressions. Copulas are used to model the dependencies over time; specifically, this paper is the first to propose using a t-copula in the context of generalized linear models. The t-copula is the copula associated with the multivariate t-distribution; like the univariate tdistributions, it seems especially suitable for empirical work. Moreover, we show that the t-copula gives rise to easily computable predictive distributions that we use to generate credibility predictors. Like Bayesian methods, our copula credibility prediction methods allow us to provide an entire distribution of predicted claims, not just a point prediction.

We present an illustrative example of Massachusetts automobile claims, and compare our new credibility estimates with those currently existing in the literature.     

Evolutionary Credibility Theory

Abstract

The conventional approach to evolutionary credibility theory assumes a linear state-space model for the longitudinal claims data so that Kalman filters can be used to estimate the claims’ expected values, which are assumed to form an autoregressive time series. We propose a class of linear mixed models as an alternative to linear state-space models for evolutionary credibility and show that the predictive performance is comparable to that of the Kalman filter when the claims are generated by a linear state-space model. More importantly, this approach can be readily extended to generalized linear mixed models for the longitudinal claims data. We illustrate its applications by addressing the “excess zeros” issue that a substantial fraction of policies does not have claims at various times in the period under consideration.     

Equity and Credibility

We build on previous work concerned with measuring equity and consider the problem of using observed claim data or other information to calculate premiums which maximize equity. When these optimal premiums are used, we show that gathering more information or refining the risk classification always increases equity. We study the case for which the premium is constrained to be an affine function of the claim data and obtain results analogous to classical credibility theory, including the inhomogeneous and homogeneous cases of the Bu¨hlmann-Straub model. We derive formulas for the credibility weights in certain cases.     

把诚信变成沉甸甸的责任

"真实无妄,始终不息,表里不杂,谓之诚;徇物无违,四端百行,必以其实,谓之信."这是古人对诚信的精辟概括.古代思想家对"人无信不立"、"国无信不兴"的宣传和弘扬,"德主刑辅"、"失礼则入刑"、"一准于礼"等中国刑法思想的儒家化,以及在礼法混同原则下违礼即犯罪,使诚信不仅是一种美德,而且是一种责任.     

Credibility for Severity Revisited

Abstract

It is basic actuarial knowledge that the pure premium of an insurance contract can be written as the product of the expected claim number and the expected claim amount. Actuaries use credibility theory to incorporate the contract’s individual experience into this calculation in a statistically optimal way. For many years, however, the use of credibility was limited to the frequency component. Starting with the paper by Hewitt (1971), there have been various suggestions as to how credibility theory also can be applied to the severity component of the pure premium. The latest such suggestion, Frees (2003), revived the interest in the problem.

In this paper, we review four different formulas incorporating frequency and severity into credibility calculations. We then compare by simulation which one is most accurate at predicting a contract’s next-year outcome. It is found that the classical formula of Bühlmann (1967) is as good as the other ones in many cases. Alternatives, however, may offer easier analysis of the separate effects of frequency and severity on the premium.

We also show that all the formulas reviewed in this paper stem from the same minimization problem, and we present a general, integrated, solution. At the same time, we complete Gerber (1972) by providing a proof to the main result of this paper and by stating required additional assumptions.     

A General Stationary Stochastic Regression Model for Estimating and Predicting Beta

A beta regression model is proposed where the coefficients follow a general class of stationary stochastic processes. The procedure identifies the process and estimates the parameters of the model simultaneously from the information contained in the return series. The returns of each of the Dow Jones 30 securities are examined. Betas of 5 of the securities are nonstationary and do not appear to follow a particular form of nonstationarity. Conclusions of many earlier studies may be suspect since they are based on procedures tailored to adoption of a specific form of beta nonstationarity and, thereby, based on an erroneous a priori assumption regarding such form. The ordinary least squares model is also found to be quite robust, providing reliable beta and intercept estimates not materially different from the more complex procedure with 25 of the return series.     

Credibility ratemaking using collateral information

Credibility ratemaking is a technique used in pricing health care, property and casualty, workers’ compensation, and group life coverages. It has been a part of actuarial practice since the time of Mowbray's (1914) contribution. In earlier work, we showed how many types of credibility models could be expressed as special cases of mixed linear models. This article extends this approach to credibility by formally introducing collateral information through the use of Bayesian methods.

Specifically, we derive credibility estimators and mean square errors for normal hierarchical linear models. We provide intuition for the credibility estimators by establishing the link between these estimators and homogeneous and inhomogeneous estimators that appear in non-Bayesian credibility theory.     

有序多分类logistic模型在违约概率测算中的应用

初始违约概率的测算是商业银行实施经济资本管理的必要环节。针对我国商业银行的现状,结合贷款五级分类,通过对银行的公司类客户的财务指标作时间加权化处理、因子分析、ROC检验以及使用有序多分类logistic模型对初始违约概率的测算作了有价值的探索,并通过算例分析论证了其可行性。     

诚信是保险企业经营的根本

诚信是市场经济的生命和灵魂,保险经营和服务必须遵循诚信原则。从经济学角度分析,保险企业必须进行诚信经营。推进保险业诚信道德建设的措施是,加强法制建设,健全相关法律体系;建立保险信用管理体系;提升保险营销人员的素质;提高服务质量,树立企业形象。     

公信力和感召力的蜕变

我记得是2009年夏天,在河北香河,《新理财》(政府理财)创刊一周年时召开座谈会。当时,参加座谈的专家、同行对这本杂记给予较高的评价并寄予厚望。现在想来,《新理财》(政府理财)创刊三年来的确呈现出比较稳定的东西—对于财政系统及其媒体来说,提供了一些新东西。在我印象里,主要体现在三个方面:一是对原有的财政媒体话语系统有所冲击,大家已经感受到这本杂志在表达方式上的新意;二是每期要有焦点类的东西呈现,类似深度报道,说     

Improving Tests of Abnormal Returns by Bootstrapping the Multivariate Regression Model with Event Parameters

Parametric dummy variable-based tests for event studies usingmultivariate regression are not robust to nonnormality of theresidual, even for arbitrarily large sample sizes. Bootstrapalternatives are described, investigated, and compared for caseswhere there are nonnormalities, and cross-sectional and time-seriesdependencies. Independent bootstrapping of residual vectorsfrom the multivariate regression model controls type I errorrates in the presence of cross-sectional correlation, and surprisingly,even in the presence of time-series dependence structures. Theproposed methods not only improve upon parametric methods, butalso allow development of new and powerful event study testsfor which there is no parametric counterpart.     

系统重要性金融机构再评估:基于最小生成树模型

评估系统重要性金融机构对于分类金融监管及防范金融风险具有重要的理论和实践价值.采用Pearson、Copula和DCC三种相关系数衡量我国91家上市金融机构的关联效应,并利用Kruskal算法构建最小生成树,研究了我国金融机构的系统重要性以及整体风险状况,研究结果表明:证券和银行在我国金融系统中的重要性更高,尤其是工商银行、广发证券和国海证券等,保险行业的系统重要性相对较弱;2015年股灾后金融机构间的关联网络发生了较大变化,银行业尤其是工商银行的系统重要性相对于股灾前得到一定提升,东方财富等新型券商开始起到重要作用;最小生成树的系统中心度可以部分反映系统性金融风险的特征,与传统系统性金融风险度量指标MES具有显著正相关性.     

Pricing Model Performance and the Two‐Pass Cross‐Sectional Regression Methodology

Over the years, many asset pricing studies have employed the sample cross‐sectional regression (CSR) R² as a measure of model performance. We derive the asymptotic distribution of this statistic and develop associated model comparison tests, taking into account the impact of model misspecification on the variability of the CSR estimates. We encounter several examples of large R² differences that are not statistically significant. A version of the intertemporal capital asset pricing model (CAPM) exhibits the best overall performance, followed by the Fama–French three‐factor model. Interestingly, the performance of prominent consumption CAPMs is sensitive to variations in experimental design.     

浅谈我国网络购物市场的诚信问题

电子商务正以前所未有的速度在发展,网上购物这种新的购物模式已经日益的深入到人们的日常生活中,并深受人们喜爱,然而伴随着网上购物的发展,其所面临的诚信问题也逐渐的被人们所重视,本文就我国当前网购市场的现状,分析了网购市场中建立诚信体系的必要性,就如何在网购市场中建立诚信体系阐明了自己的观点.     

经典回归与稳健回归方法的应用比较研究

本文首先给出基于传统统计方法的经典回归方法中存在的一些不足,然后提出稳健回归方法的应用并通过实证计算与经典回归进行对比分析,最后对两种回归方法进行应用总结,得出稳健回归方法在抵御数据中的离群值方面具有最小二乘回归所无可比拟的优越性的结论。但是由于稳健统计方法通俗性比较差,使得经典统计方法的地位始终无法动摇。因此,在实际运用中,尽可能综合使用经典的和稳健的统计方法,从而达到既能够准确掌握问题主体部分的信息,同时又不会忽略对非主体信息的充分挖掘。     

张智勇:千心铸信,稳健百年

虽然成立仅八年时间, 但长沙市商业银行取得的 成就足以让业界瞩目:对公 业务、个人业务始终以年均 30％以上的增长率高速发 展;全行资产总额、存款余 额和贷款余额分别比成立 之初增长了9倍、7倍和6倍。 与此同时,长沙市商业银行 在《银行家》杂志5月份举 行的城市商业银行排名中, 无论是资产规模,存款余     

基于逻辑回归的企业大额可疑外汇资金交易识别模型

本文根据逻辑回归原理与数据挖掘技术,建立了企业大额可疑外汇资金交易识别模型,用于分析银行企业客户洗钱的概率及洗钱事件发生的可能性。本文的目的是通过对具有洗钱嫌疑的银行企业客户进行识别和预测,为银行反洗钱技术提供参考。     

运用Logistic回归模型加强高收入者纳税遵从的实证研究

加强高收入者的个人所得税征管、促进纳税遵从一直是税务部门的重要工作之一。利用多元有序因变量Logistic回归模型,以江苏某市2010年度年所得12万元以上个人所得税纳税申报的数据为样本,以＂应补税额＂等级的五分类有序变量为因变量,以纳税申报表中纳税人的年龄、应纳税所得额、应纳税额、性别、职业大类、行业大类6个影响因素为自变量,进行多元有序因变量的Logistic回归分析,研究结果可为税务系统加强年所得12万元以上高收入者个人所得税的申报与征管、促进纳税遵从提供新的思路。