行驶里程数对车险净保费的影响研究 ——基于公路里程对交通事故损失的影响视角

目前国内几乎所有财险公司的数据库中还没有行驶里程数的统计数据。文章首次研究了行驶里程数对车险净保费的影响,即利用我国2000年～2009年31个省、市、自治区10年的面板数据单位根检验、协整检验等计量经济学方法来研究交通事故损失额与公路里程数之间长期稳定的均衡关系,得出事故损失额与公路里程数之间存在显著正相关关系。本研究的应用价值在于,该相关关系可以作为车险净保费与行驶里程数之间关系的有效参考,并提出了考虑车险净保费与行驶里程数之间关系的三种可行方案。这些研究为将行驶里程数这一影响因素纳入我国车险GLM定价提供了重要的理论支持和实践参考,也对解决我国交通、能源和环境问题具有一定的借鉴作用。     

基于双重广义线性模型的车险费率厘定及其与广义线性模型的比较

在车险费率厘定中,广义线性模型的应用最为广泛,然而其假设散度参数为常值,这限制了模型在车险定价中的进一步推广。双重广义线性模型能够对反应变量的均值与散度参数同时建立广义线性模型,提高了模型运用的灵活性与适应性。本文将双重广义线性模型应用到车险费率厘定中,直接对纯保费建立模型,以一组实际的汽车保险损失数据为样本进行实证研究,并与常用分布假设下的广义线性模型进行了对比分析。结果表明,双重广义线性模型得到的费率结构更为合理,符合实际。     

基于累积损失混合模型的贝叶斯保费研究

商业车险的费率由先验费率和后验费率两部分构成。通常使用广义线性模型厘定先验费率,然后基于个体保单的索赔经验,应用贝叶斯方法计算后验费率。在传统方法中,一般是分别根据索赔次数或索赔强度建立费率厘定模型。本文基于个体保单的累积损失数据建立了一种混合回归模型,并在此基础上计算贝叶斯保费,为非寿险费率厘定提供了一种新方法。在先验费率的厘定中,基于个体保单的累积损失数据建立混合零调整逆高斯回归模型,代替了传统的Tweedie回归模型。对先验费率进行调整时,用个体保单的累积损失代替通常使用的索赔次数或索赔强度,规避了索赔次数与索赔强度之间的相依性可能造成的干扰。     

考虑模型不确定性的中国死亡率预测——基于贝叶斯模型平均方法

无赔款优待系统是车险定价中的基本工具。在实务中,只有当发生的损失较大时,投保人才提出索赔,此时损失由保险人承担,但索赔可能会导致未来保费的上升。当发生的损失较小(或没有损失时),投保人不提出索赔,此时损失由投保人承担,无索赔可能会导致未来保费的下降。因此存在损失临界值(称为隐含免赔额),使得投保人未来各年度保费和自行承担损失的现值最小。最优索赔策略等价于各个保费等级对应的损失临界值。最后,本文使用我国2015年商业车险费率改革后的有关数据,分别在损失额服从指数分布和伽马分布的假设下,计算出各保费等级的隐含免赔额,并定量分析在指数分布假设下不同贴现率对隐含免赔额和无索赔概率的影响。     

道路交通事故后果与我国交强险奖惩系统的构建与评价北大核心CSSCI

为实现车险高质量发展,2020年9月银保监会发布《关于实施车险综合改革的指导意见》,要求提升交强险保障水平,并通过在奖惩系统中增加区域浮动因子提高交强险费率厘定的科学性与公平性。被保险人所引致的道路交通事故后果与其风险水平高度相关,而现行的交强险奖惩系统并未考虑该风险因素。本文根据《公安部关于修订道路交通事故等级划分标准的通知》,将道路交通事故按后果分为轻微、一般和重大事故,结合区域特征与索赔次数等信息,构建一种新的奖惩系统。选取稳态下相对平均保费水平、稳态变化率等指标对新构建的奖惩系统进行评价,并以一组交强险实际赔付数据为例,进行实证分析。研究结果表明考虑道路交通事故后果的奖惩系统可以更好地区分风险,优化交强险后验费率厘定的效果。     

广义估计方程在商业车险定价中的应用

2015年4月中国保监会在全国六个地区进行商业车险费率改革试点,标志着商业车险市场化改革正式启动。费率市场化改革后,车险定价是否合理将成为财产保险公司竞争的主要手段。在车险定价中常用的模型是广义线性模型,该模型建立的一个重要假设是索赔数据的相互独立性。但在实践中,随着投保年份的增加,同一投保人不同年份的索赔数据具有相关性,此时广义线性模型不再适用。本文采用广义估计方程来处理索赔数据之间的相关性,实证研究表明,在数据具有相关性的情况下,广义线性模型低估了回归系数的标准差,使得不显著的变量变得显著,增加了风险分类的种类,对具有相同风险的被保险人收取不同的保费,导致保险逆选择问题,而广义估计方程将二阶方差成分引入限制性似然估计方程中处理索赔数据之间的相关性,从而有效解决上述问题。同时,该方法也丰富了非寿险定价工具,为精算师厘定费率提供新思路。     

我国商业车险奖惩系统研究

商业车险的费率主要由先验费率和浮动费率两部分构成。先验费率通常使用广义线性模型进行厘定,而浮动费率则是通过奖惩系统(Bonus-Malus System,BMS)对先验费率进行的一种后验调整。我国现行的商业车险BMS存在转移规则不够合理和奖惩系数不尽准确的问题。本文使用动态转移规则,在线性约束下,通过最小化索赔频率真实值与预测值之间的均方误差,求得了BMS的最优奖惩系数,并基于我国某财产保险公司2015年的一组商业车险数据进行了实证研究。结果表明,本文的方法可以有效改善我国现行商业车险BMS存在的不足。     

Tweedie分布在车险费率厘定中的应用

在车险费率厘定中经常假设索赔频率与索赔强度分别服从泊松分布与伽玛分布,即假设总索赔服从复合泊松-伽玛分布。为了估计各风险类的纯保费(即总索赔均值),通常做法是对索赔频率与索赔强度分别建立广义线性模型(GLM),进而得到各风险类的索赔频率与索赔强度的均值,然后把两均值简单相乘即可;另一种做法利用复合泊松-伽玛分布是Tweedie分布的特例这一性质,直接对总索赔建立广义线性模型,进而也可以得到各风险类的总索赔均值。本文阐述了两种建模方法在处理车险费率厘定问题时的区别,通过对来自国外、国内的两组数据进行实证分析,比较了两种建模方法的优劣,并得到了一些初步结论。     

基于厚尾损失分布的汽车保险定价模型及其应用

我国目前正在推进商业车险费率的市场化改革,这要求保险公司使用更加准确的风险度量方法和损失预测模型。在汽车保险中,损失的厚尾性对费率厘定和风险管理都具有重要影响。本文引入密度函数的极限方法刻画损失分布的厚尾特征,构建二型广义贝塔分布下的GAMLSS定价模型,以改进传统广义线性模型中的指数族分布假设和只能对均值参数建模的局限。通过对国内商业车险损失数据的实证分析表明,使用厚尾分布假设和GAMLSS定价模型,可以提高汽车保险损失的预测精度,从而厘定更加合理的保险费率。     

我国车险市场承保周期研究——基于费率管制与市场准入限制的影响

对车险承保周期的研究,传统上是从“价”的角度着手,以单位价格（保费/赔付额）和承保利润率为指标,来考察承保周期的波动特征。然而,我国车险市场中存在两个特殊的局限条件：费率管制和市场准入限制。费率管制的存在,使保费收入不能反映车险业务的真实情况,从而以保费为基础的传统研究指标也不能用于对我国车险市场的研究。基于此,本文转换分析的角度,从“量”入手,以赔付额来描述车险市场的承保周期。研究发现,我国车险市场存在承保周期,周期平均长度为533年,并且市场准入限制是影响车险承保周期的重要原因。     

Case Studies Using Panel Data Models

Abstract

In this paper, we examine case studies from three different areas of insurance practice: health care, workers’ compensation, and group term life. These different case studies illustrate how the broad class of panel data models can be applied to different functional areas and to data that have different features. Panel data, also known as longitudinal data, models are regression-type models that have been developed extensively in the biological and economic sciences. The data features that we discuss include heteroscedasticity, random and fixed effect covariates, outliers, serial correlation, and limited dependent variable bias. We demonstrate the process of identifying these features using graphical and numerical diagnostic tools from standard statistical software.

Our motivation for examining these cases comes from credibility rate making, a technique for pricing certain types of health care, property and casualty, workers’ compensation, and group life coverages. It has been a part of actuarial practice since Mowbray’s (1914) fundamental contribution. In earlier work, we showed how many types of credibility models could be expressed as special cases of panel data models. This paper exploits this link by using tools developed in connection with panel data models for credibility rate-making purposes. In particular, special routines written for credibility rate-making purposes are not required.     

Number of Accidents or Number of Claims? An Approach with Zero‐Inflated Poisson Models for Panel Data

The  hunger for bonus  is a well-known phenomenon in insurance, meaning that the insured does not report all of his accidents to save bonus on his next year's premium. In this article, we assume that the number of accidents is based on a Poisson distribution but that the number of claims is generated by censorship of this Poisson distribution. Then, we present new models for panel count data based on the zero-inflated Poisson distribution. From the claims distributions, we propose an approximation of the accident distribution, which can provide insight into the behavior of insureds. A numerical illustration based on the reported claims of a Spanish insurance company is included to support this discussion.     

Hourly changes in accident risk for bus drivers

Traffic accident risk has in some studies been found to change with the time of day, after controlling for exposure, probably due to diurnal changes in the human body, which changes alertness. However, exposure data are not always of good quality, and culpability for accidents is not always taken into account. The change in culpable accident risk over the day for bus drivers was therefore investigated, with single accidents analysed separately, using induced exposure (non‐culpable bus accidents) as well as general traffic density and number of buses on the road as controlling factors. It was found that the risk distribution was fairly similar to some previous results before controlling for exposure, but dissimilar to other, probably indicating that bus drivers have a somewhat different risk profile, but also that previous studies may not have controlled for exposure in a reliable way. When exposure was held constant, the risk distribution was different from all other studies. The three different exposure measures correlated strongly between themselves, and each would seem to be adequate for a basic control. However, although general traffic density was most strongly correlated with culpable bus accidents, the induced exposure parameter added some explained variance. Single accidents had a very different risk distribution as compared to other culpable accidents when exposure had been held constant. A number of unexpected effects were also noted, mainly that single accidents were associated most strongly with general traffic density.     

An application of two-stage quantile regression to insurance ratemaking

Two-part models based on generalized linear models are widely used in insurance rate-making for predicting the expected loss. This paper explores an alternative method based on quantile regression which provides more information about the loss distribution and can be also used for insurance underwriting. Quantile regression allows estimating the aggregate claim cost quantiles of a policy given a number of covariates. To do so, a first stage is required, which involves fitting a logistic regression to estimate, for every policy, the probability of submitting at least one claim. The proposed methodology is illustrated using a portfolio of car insurance policies. This application shows that the results of the quantile regression are highly dependent on the claim probability estimates. The paper also examines an application of quantile regression to premium safety loading calculation, the so-called Quantile Premium Principle (QPP). We propose a premium calculation based on quantile regression which inherits the good properties of the quantiles. Using the same insurance portfolio data-set, we find that the QPP captures the riskiness of the policies better than the expected value premium principle.     

Aircraft safety analysis using clustering algorithms

In recent years, there have been many cost-benefit studies on aviation safety, which deal mainly with economic issues, omitting some strictly technical aspects. This study compares aircraft accidents in relation to the characteristics of the aircraft, environmental conditions, route, and traffic type. The study was conducted using a database of over 1500 aircraft accidents worldwide, occurring between 1985 and 2010. The data were processed and then aggregated into groups, using cluster analysis based on an algorithm of partition binary ‘Hard c means.’ For each cluster, the ‘cluster representative’ accident was identified as the average of all the different characteristics of the accident. Moreover, a ‘hazard index’ was defined for each cluster (according to annual movements); using this index, it was possible to establish the dangerousness of each ‘cluster’ in terms of aviation accidents. Obtained results allowed the construction of an easy-to-use predictive model for accidents using multivariate analysis.     

On the Consequences of Behavioral Adaptations in the Cost–Benefit Analysis of Road Safety Measures

It is sometimes argued that road safety measures or automobile safety standards fail to save lives because safer highways or safer cars induce more dangerous driving. A similar but less extreme view is that ignoring the behavioral adaptation of drivers would bias the cost–benefit analysis of a traffic safety measure. This article derives cost–benefit rules for automobile safety regulation when drivers may adapt their risk‐taking behavior in response to changes in the quality of the road network. The focus is on the financial externalities induced by accidents because of the insurance system as well as on the consequences of drivers' risk aversion. We establish that road safety measures are Pareto improving if their monetary cost is lower than the difference between their (adjusted for risk aversion) direct welfare gain with unchanged behavior and the induced variation in insured losses due to drivers' behavioral adaptation. The article also shows how this rule can be extended to take other accident external costs into account.     

索赔特征对保险理赔(诉讼)额影响的实证分析——基于交强险人身伤害判决数据

面对日益增多的保险理赔(诉讼),亟需加强索赔原因及索赔特征对法院判决结果的影响研究.本文通过对北京市大兴区人民法院2007年1月至2010年8月涉及人身伤害的交强险判决案例进行回归分析,发现:索赔原因与索赔人损失大小、就业状况、法律规定的赔偿上限有关;索赔人在交通事故中承担的过错责任与其性别、医疗费支出状况、是否死亡有...     

Automobile Insurance Contracts and Risk of Accident: An Empirical Test Using French Individual Data

Insurance has for a long time been perceived as a way of transferring responsibility from insured agents to insurers and thus as potentially influencing insured agents' behavior. Two particular opportunistic behaviors have been analyzed. First, the theory of adverse selection predicts that high-risk agents are likely to demand more insurance than are low-risk agents. Second, the theory of moral hazard predicts that the wider the insurance coverage, the less agents will try to prevent accidents. Both theories thus conclude that agents who are totally insured should have a higher probability of accident than those with only partial insurance, ceteris paribus. Nevertheless, one of the aims of insurance rating systems is to control for these opportunistic behaviors. In this article, we use individual data to see if the French automobile insurance rating system has achieved this aim. We do this using a two-step maximum-likelihood method. First, we compute a probit model to estimate the probability of taking out comprehensive versus third-party insurance. We then calculate the generalized residual, which is included as an independent variable in a negative binomial model estimating the probability of having an accident. The coefficient of this variable is argued to represent adverse selection and ex-ante moral-hazard behavior.     

The Effects of Regulated Premium Subsidies on Insurance Costs: An Empirical Analysis of Automobile Insurance

State regulation of rates is sometimes used as a means to make automobile insurance more affordable to consumers by restricting insurer profits and pricing practices. Incentive distortions arising from this type of rate regulation might lead to higher accident rates and higher insurance loss costs. Annual state‐level panel data for the time period 1980–1998 are used to investigate these effects, using empirical methods that recognize the endogenous determination of states’ regulatory choices. Results suggest that rate regulation that systematically suppresses (some or all) drivers’ insurance premiums is associated with significantly higher average loss costs and higher insurance claim frequency.