基于广义线性混合模型的经验费率厘定

信度模型是非寿险精算学中最为重要的成果.从20世纪初至今,信度理论先后经历了两个发展阶段:一是早期的有限波动信度模型;二是目前的最大精确信度模型.有限波动信度模型强调结果的稳定性,而最大精确信度模型强调结果的精确性.因此建立信度模型与广义线性混合模型之间的联系,通过对信度模型的分解可以看到:传统的信度理论对风险的刻画方法与广义线性混合模型的结构有极其相似的地方,故可以用广义线性混合模型来厘定经验费率.     

基于分层广义线性模型的非寿险费率厘定精算模型研究

非寿险业务中的损失数据结构日益复杂,呈现异质性与相关性并存的异象。分层广义线性模型能够突破传统费率厘定精算方法仅分析风险个体同一保单年损失数据的局限,可以提高复杂结构损失数据预测的准确性。基于分层广义线性模型等方法,研究具有多年损失数据的非寿险费率厘定问题,并以车险和工伤补偿保险的两组损失数据为例进行实证分析。研究结果表明,相对于GLM而言,考虑随机效应后GLMM的拟合优度大幅改善,GLMM与HGLM可以更有效地反映不同风险个体的差异,并有利于揭示风险个体在多个保险期内损失的异质性与相关性。     

分位数回归在非寿险产品费率厘定中的应用

文章首先分析了非寿险产品费率厘定中的零索赔额现象;指出了线性回归模型和广义线性模型在非寿险产品费率厘定中存在的问题和不足;分析了分位数回归模型在非寿险产品费率厘定中的优点,并结合实例,给出了实证分析.结果表明,分位数回归模型更能从整体上反映出费率厘定变量之间的关系及其对索赔额的影响.     

广义线性模型在非寿险精算中的应用及其研究进展

广义线性模型在精算中的应用始于20世纪80年代，其应用涉及到精算学的各个领域，如生命表的修匀、损失分布、信度理论、风险分类、准备金和费率估计等方面。在对广义线性模型适用于非寿险精算的典型特征进行分析的基础上，对广义线性模型在非寿险精算中的应用及其研究进展进行分析和总结的同时，重点分析利率厘定和准备金估计中广义线性模型的建模思想，并结合实际提出了今后研究的方向。     

基于贝叶斯偏态线性混合模型的费率厘定

线性混合模型是非寿险费率厘定的主要方法之一。通常的线性混合模型假设随机误差项服从正态分布,而保险损失数据往往具有右偏特征,这使得该模型在非寿险费率厘定中的应用受到一定影响。在通常的线性混合模型基础上,假设随机误差项服从偏态分布,即可建立偏态线性混合模型,从而改善费率厘定结果的合理性。基于一组实际的保险损失数据,应用贝叶斯MCMC方法建立几个不同的偏态线性混合模型,并与正态分布假设下的线性混合模型进行对比,实证检验偏态线性混合模型在非寿险费率厘定中的优越性。     

基于广义线性模型的交强险费率厘定研究

文章利用广义线性模型对我国现行交强险费率体系进行了研究,结果发现,现存的风险分级方法过于简单,保单持有人之间存在很大的不公平.因此,有必要采取更多的费率因子.     

广义线性混合模型及其在非寿险信度费率厘定中的应用

近年来,国内外精算学者开始将广义线性混合模型用于信度模型费率厘定中,但他们对因变量的推广仅仅推广到负二项分布。在前人的研究基础上,将因变量进一步推广到负二项K、广义泊松、双泊松等分布,然后用极大似然估计中的限制性虚拟似然法和自适应高斯求积法对参数进行估计,最后用美国劳工补偿保险进行实证分析。结果表明:负二项K(K=1.947)广义线性混合模型对数据拟合效果最好,其次为负二项1、负二项2、双泊松、广义泊松和泊松广义线性混合模型。     

Hurdle模型在非寿险分类费率厘定中的应用

泊松回归模型是常用的索赔次数预测模型。但在实务中,索赔次数往往具有零膨胀特征,如果继续使用泊松模型会低估参数的标准误差,高估其显著性水平,从而在模型中保留多余的解释变量,产生不准确费率厘定结果。Hurdel模型是一个二阶段模型,可以将索赔次数分为两个部分来处理。因此,利用该模型的这一性质来处理费率厘定中具有零膨胀特征的索赔数据,可以有效地改善拟合效果。     

广义线性滤波模型在非寿险准备金评估中的应用

文章在非寿险未决赔款准备金评估中,借鉴状态空间模型如Kalman滤波在准备金评估中的应用,以广义线性模型为基础,通过在贝叶斯估计中利用泰勒展开式的二阶近似式构造了离散指数族内的后验似然函数,生成广义线性滤波,可实现动态广义线性模型的参数估计,从而能够向模型中引入新的观测数据递归出更新的参数估计结果。文章通过实例演示了伽玛广义线性滤波模型在准备金评估中的应用。     

广义线性模型的性质及其在非寿险中的应用

广义线性模型的误差项服从指数分布族,通常的指数分布族包括正态分布、泊松分布、二项分布、伽玛分布、逆高斯分布等,这些分布模型在非寿险精算中都有广泛的应用。在对上述常见模型特点分析的同时,用实际数据进行了拟合,为精算师在实务工作中提供了些建议。     

非寿险费率厘定的索赔频率预测模型及其应用

在非寿险分类费率厘定中,泊松回归模型是最常使用的索赔频率预测模型,但实际的索赔频率数据往往存在过离散特征,使泊松回归模型的结果缺乏可靠性.因此,讨论处理过离散问题的各种回归模型,包括负二项回归模型、泊松-逆高斯回归模型、泊松-对数正态回归模型、广义泊松回归模型、双泊松回归模型、混合负二项回归模型、混合二项回归模型、Delaporte回归模型和Sichel回归模型,并对其进行系统比较研究认为:这些模型都可以看做是对泊松回归模型的推广,可以用于处理各种不同过离散程度的索赔频率数据,从而改善费率厘定的效果;同时应用一组实际的汽车保险数据,讨论这些模型的具体应用.     

Estimation of the Predictive Ability of Ecological Models

The conventional criteria for predictive model selection do not indicate the absolute goodness of models. For example, the quantity of Akaike Information Criterion (AIC) has meanings only when we compare AIC of different models for a given amount of data. Thus, the existing criteria do not tell us whether the quantity and quality of data is satisfactory, and hence we cannot judge whether we should collect more data to further improve the model or not. To solve such a practical problem, we propose a criterion R_D that lies between 0 and 1. R_D is an asymptotic estimate of the proportion of improvement in the predictive ability under a given error structure, where the predictive ability is defined by the expected logarithmic probability by which the next dataset (2nd dataset) occurs under a model constructed from the current dataset (1st dataset). That is, the predictive ability is defined by the expected logarithmic probability of the 2nd dataset evaluated at the model constructed from the 1st dataset. Appropriate choice of error structures is important in the calculation of R_D. We illustrate examples of calculations of R_D by using a small dataset about the moth abundance.     

联合广义线性模型中的变量选择

在联合广义线性模型中,散度参数与均值都被赋予了广义线性模型的结构,本文主要考虑在只有分布的一阶矩和二阶矩指定的条件下,联合广义线性模型中均值部分的变量选择问题。本文采用广义拟似然函数,提出了新的模型选择准则(EAIC);该准则是Akaike信息准则的推广。论文通过模拟研究验证了该准则的效果。     

Tuning Parameter Selector for the Penalized Likelihood Method in Multivariate Generalized Linear Models

Variable selection is fundamental to high-dimensional multivariate generalized linear models. The smoothly clipped absolute deviation (SCAD) method can solve the problem of variable selection and estimation. The choice of the tuning parameter in the SCAD method is critical, which controls the complexity of the selected model. This article proposes a criterion to select the tuning parameter for the SCAD method in multivariate generalized linear models, which is shown to be able to identify the true model consistently. Simulation studies are conducted to support theoretical findings, and two real data analysis are given to illustrate the proposed method.     

Generalized Additive Modelling of Mixed Distribution Markov Models with Application to Melbourne's Rainfall

The paper considers the modelling of time series using a generalized additive model with first-order Markov structure and mixed transition density having a discrete component at zero and a continuous component with positive sample space. Such models have application, for example, in modelling daily occurrence and intensity of rainfall, and in modelling numbers and sizes of insurance claims. The paper shows how these methods extend the usual sinusoidal seasonal assumption in standard chain-dependent models by assuming a general smooth pattern of occurrence and intensity over time. These models can be fitted using standard statistical software. The methods of Grunwald & Jones (2000) can be used to combine these separate occurrence and intensity models into a single model for amount. The models are used to investigate the relationship between the Southern Oscillation Index and Melbourne's rainfall, illustrated with 36 years of rainfall data from Melbourne, Australia.     

A Simulation-based Goodness-of-fit Test for Random Effects in Generalized Linear Mixed Models

Abstract.  The goodness-of-fit of the distribution of random effects in a generalized linear mixed model is assessed using a conditional simulation of the random effects conditional on the observations. Provided that the specified joint model for random effects and observations is correct, the marginal distribution of the simulated random effects coincides with the assumed random effects distribution. In practice, the specified model depends on some unknown parameter which is replaced by an estimate. We obtain a correction for this by deriving the asymptotic distribution of the empirical distribution function obtained from the conditional sample of the random effects. The approach is illustrated by simulation studies and data examples.     

Estimation of the Force of Infection from Current Status Data Using Generalized Linear Mixed Models

Based on sero-prevalence data of rubella, mumps in the UK and varicella in Belgium, we show how the force of infection, the age-specific rate at which susceptible individuals contract infection, can be estimated using generalized linear mixed models (McCulloch & Searle, 2001). Modelling the dependency of the force of infection on age by penalized splines, which involve fixed and random effects, allows us to use generalized linear mixed models techniques to estimate both the cumulative probability of being infected before a given age and the force of infection. Moreover, these models permit an automatic selection of the smoothing parameter. The smoothness of the estimated force of infection can be influenced by the number of knots and the degree of the penalized spline used. To determine these, a different number of knots and different degrees are used and the results are compared to establish this sensitivity. Simulations with a different number of knots and polynomial spline bases of different degrees suggest - for estimating the force of infection from serological data - the use of a quadratic penalized spline based on about 10 knots.