零膨胀广义泊松回归模型与保险费率厘定

在保险产品的分类费率厘定中,最常使用的模型之一是泊松回归模型.当损失数据存在零膨胀(zero-in flated)特征时,通常会采用零膨胀泊松回归模型.在零膨胀泊松回归模型中,一般假设结构零的比例参数φ为常数,不受费率因子的影响,这有可能背离实际情况.假设参数φ与费率因子之间存在一定关系,并在此基础上建立了零膨胀广义泊松回归模型,即Z IGP(τ)回归模型.通过对一组汽车保险损失数据的拟合表明,Z IGP(τ)回归模型可以有效地改善对实际数据的拟合效果,从而提高费率厘定结果的合理性.     

Bayesian quantile regression model for claim count data

Quantile regression model estimates the relationship between the quantile of a response distribution and the regression parameters, and has been developed for linear models with continuous responses. In this paper, we apply Bayesian quantile regression model for the Malaysian motor insurance claim count data to study the effects of change in the estimates of regression parameters (or the rating factors) on the magnitude of the response variable (or the claim count). We also compare the results of quantile regression models from the Bayesian and frequentist approaches and the results of mean regression models from the Poisson and negative binomial. Comparison from Poisson and Bayesian quantile regression models shows that the effects of vehicle year decrease as the quantile increases, suggesting that the rating factor has lower risk for higher claim counts. On the other hand, the effects of vehicle type increase as the quantile increases, indicating that the rating factor has higher risk for higher claim counts.     

Capture-Recapture模型与车险事故总体预测

车险事故总体预测问题一直是车辆保险公司研究的重点内容之一,目前最为常用的方法是与泊松分布相关的模型.基于车辆保险中索赔数据的结构特征,构建了Capture-Recapture模型,并使用一组车辆保险数据,利用Capture-Recapture及常用的零膨胀泊松等模型分别建模分析,得出了一些新的结论,即Capture-Recapture模型拟合效果整体较优,从而为车辆保险公司更好预测事故总体提供一定的理论依据.     

Explaining functional principal component analysis to actuarial science with an example on vehicle insurance

Given the high competitiveness in the vehicle insurance market, the need arises for an adequate pricing policy. To this end, insurance companies must select risks in a way that allows the expected claims ratio to come as close as possible to the real claims ratio. The use of new analytical tools which provide more information is of great interest. In this paper it is shown how functional principal component analysis can be useful in actuarial science. An empirical study is carried out with data from a Spanish insurance company to estimate the risk of occurrence of a claim in terms of the driver’s age, whilst taking into account other relevant variables.     

Nonlife ratemaking and risk management with Bayesian generalized additive models for location,scale, and shape

Generalized additive models for location, scale and, shape define a flexible, semi-parametric class of regression models for analyzing insurance data in which the exponential family assumption for the response is relaxed. This approach allows the actuary to include risk factors not only in the mean but also in other key parameters governing the claiming behavior, like the degree of residual heterogeneity or the no-claim probability. In this broader setting, the Negative Binomial regression with cell-specific heterogeneity and the zero-inflated Poisson regression with cell-specific additional probability mass at zero are applied to model claim frequencies. New models for claim severities that can be applied either per claim or aggregated per year are also presented. Bayesian inference is based on efficient Markov chain Monte Carlo simulation techniques and allows for the simultaneous estimation of linear effects as well as of possible nonlinear effects, spatial variations and interactions between risk factors within the data set. To illustrate the relevance of this approach, a detailed case study is proposed based on the Belgian motor insurance portfolio studied in Denuit and Lang (2004).     

负二项回归模型的推广及其在分类费率厘定中的应用

分类费率厘定中最常使用的模型之一是泊松回归模型,但当损失次数数据存在过离散特征时,通常会采用负二项回归模型。本文将两参数的负二项回归模型推广到了三参数情况,并用它来解决分类费率厘定中的过离散(over-dispersion)问题。本文通过对一组汽车保险损失数据的拟合表明,三参数的负二项分布回归模型可以有效改善对实际损失数据的拟合效果。     

Forecasting retained earnings of privately held companies with PCA and L1 regression

We use proprietary data collected by SVB Analytics, an affiliate of Silicon Valley Bank, to forecast the retained earnings of privately held companies. Combining methods of principal component analysis (PCA) and L¹/quantile regression, we build multivariate linear models that feature excellent in‐sample fit and strong out‐of‐sample predictive accuracy. The combined PCA and L¹ technique effectively deals with multicollinearity and non‐normality of the data, and also performs favorably when compared against a variety of other models. Additionally, we propose a variable ranking procedure that explains which variables from the current quarter are most predictive of the next quarter's retained earnings. We fit models to the top five variables identified by the ranking procedure and thereby, discover interpretable models with excellent out‐of‐sample performance. Copyright © 2013 John Wiley & Sons, Ltd.     

Confidence bands in nonparametric regression with length biased data

In this paper we deduce a confidence bands construction for the nonparametric estimation of a regression curve from length biased data, where a result from Bickel and Rosenblatt (1973,The Annals of Statistics,1, 1071–1095) is adapted to this new situation. The construction also involves the estimation of the variance of the local linear estimator of the regression, where we use a finite sample modification in order to improve the performance of these confidence bands in the case of finite samples.     

A DEA analysis of risk,cost, and revenues in insurance

Insurance companies have to take risk and cost into account when pricing car insurance policies that cover the risk of private use of cars. In this paper we use data from 80?000 car insurance policies in order to assess, once risk and cost have been taken into account, the combinations of risk that generate the highest returns for the company under existing pricing practices. We use data envelopment analysis (DEA) and frame the study within an analysis of experiments context. The results of DEA are interpreted in a multivariate statistical analysis context using factor analysis, and property fitting techniques. The impact of risk factors in the efficiency is explored by means of regression analysis with dummy variables. There are consequences for the pricing policy of the company.     

Hazard Rate Regression Using Ordinary Nonparametric Regression Smoothers

Abstract

This article proposes a method for nonparametric estimation of hazard rates as a function of time and possibly multiple covariates. The method is based on dividing the time axis into intervals, and calculating number of event and follow-up time contributions from the different intervals. The number of event and follow-up time data are then separately smoothed on time and the covariates, and the hazard rate estimators obtained by taking the ratio. Pointwise consistency and asymptotic normality are shown for the hazard rate estimators for a certain class of smoothers, which includes some standard approaches to locally weighted regression and kernel regression. It is shown through simulation that a variance estimator based on this asymptotic distribution is reasonably reliable in practice. The problem of how to select the smoothing parameter is considered, but a satisfactory resolution to this problem has not been identified. The method is illustrated using data from several breast cancer clinical trials.     

Treed Regression

Abstract

Given a data set consisting of n observations on p independent variables and a single dependent variable, treed regression creates a binary tree with a simple linear regression function at each of the leaves. Each node of the tree consists of an inequality condition on one of the independent variables. The tree is generated from the training data by a recursive partitioning algorithm. Treed regression models are more parsimonious than CART models because there are fewer splits. Additionally, monotonicity in some or all of the variables can be imposed.     

基于因子分析的中国寿险公司经营效率综合评价

利用财务指标法评价寿险公司绩效的一个重要特点就是主观赋权,而主观赋权一方面会导致对某个或某些因素过高或过低的估计,使评价结果不能如实反映寿险公司的真实情况,另一方面会诱使寿险公司粉饰或追求权重较高的指标.利用因子分析法,以2007年在我国境内开展业务的34家寿险公司作为样本,选择17个指标构建截面数据体系,对样本公司的风险水平和经营绩效进行评价.结果表明,老牌中资寿险公司保持着强大的综合实力,仍然是我中国人寿险市场的主导;外资寿险公司逐步加大规模扩张,资产管理能力不容轻视.     

基于模糊理论的机动车辆风险评估

对机动车辆风险进行评估是车险费率厘定的一个重要环节.提出一种基于模糊理论的机动车辆风险评估方法(The Risk Assess of Motor Vehicle Based on Fuzzy Theory,简称RMFT),应用表明该方法在风险评估的精度上取得较好效果.     

Predicting ships' CO2 emissions using feature‐oriented methods

Shipping companies are forced by the current EU regulation to set up a system for monitoring, reporting, and verification of harmful emissions from their fleet. In this regulatory background, data collected from onboard sensors can be utilized to assess the ship's operating conditions and quantify its CO₂ emission levels. The standard approach for analyzing such data sets is based on summarizing the measurements obtained during a given voyage by the average value. However, this compression step may lead to significant information loss since most variables present a dynamic profile that is not well approximated by the average value only. Therefore, in this work, we test two feature‐oriented methods that are able to extract additional features, namely, profile‐driven features (PdF) and statistical pattern analysis (SPA). A real data set from a Ro‐Pax ship is then considered to test the selected methods. The data set is segregated according to the voyage distance into short, medium, and long routes. Both PdF and SPA are compared with the standard approach, and the results demonstrate the benefits of employing more systematic and informative feature‐oriented methods. For the short route, no method is able to predict CO₂ emissions in a satisfactory way, whereas for the medium and long routes, regression models built using features obtained from both PdF and SPA improve their prediction performance. In particular, for the long route, the standard approach failed to provide reasonably good predictions.     

Parametric multiple regression risk models: Connections with tariffication,especially in motor insurance

It is shown how the parametric multiple regression risk models of Albrecht (1983a) can be used for solving the problem of tariffication of e.g. an motor insurance portfolio.     

Detecting fuzzy relationships in regression models: The case of insurer solvency surveillance in Germany

We develop a test for the fuzziness of regression coefficients based on the Tanaka et al. (1982) and He et al. (2007) possibilistic fuzzy regression models. We interpret the spread of the regression coefficients as a statistic measuring the fuzziness of the relationship between the corresponding independent variable and the dependent variable. We derive test distributions based on the null hypothesis that such spreads could have been obtained by estimating a possibilistic regression with data generated by a classical regression model with random errors. As an example, we show how our test detects a fuzzy regression coefficient in a solvency prediction model for German property-liability insurance companies.     

L1正则化Logistic回归在财务预警中的应用

线性模型和广义线性模型已广泛地用于社会经济、生产实践和科学研究中的数据分析和数据挖掘等领域,如公司财务预警,引入L1范数惩罚技术的模型在估计模型系数的同时能实现变量选择的功能,本文将L1范数正则化Logistic回归模型用于上市公司财务危机预报,结合沪深股市制造业ST公司和正常公司的T-2年财务数据开展实证研究,舛比Logistic回归和L2正则化Logistic回归模型进行对比分析.实验结果表明L1正则化Logistic回归模型的有效性,其在保证模型预测精度的同时提高模型的解释性.     

A Fast and Stable Updating Algorithm for Bivariate Nonparametric Curve Estimation

Abstract

An updating algorithm for bivariate local linear regression is proposed. Thereby, we assume a rectangular design and a polynomial kernel constrained to rectangular support as weight function. Results of univariate regression estimators are extended to the bivariate setting. The updates are performed in a way that most of the well-known numerical instabilities of a naive update implementation can be avoided. Some simulation results illustrate the properties of several algorithms with respect to computing time and numerical stability.     

Randomized Quantile Residuals

Abstract

In this article we give a general definition of residuals for regression models with independent responses. Our definition produces residuals that are exactly normal, apart from sampling variability in the estimated parameters, by inverting the fitted distribution function for each response value and finding the equivalent standard normal quantile. Our definition includes some randomization to achieve continuous residuals when the response variable is discrete. Quantile residuals are easily computed in computer packages such as SAS, S-Plus, GLIM, or LispStat, and allow residual analyses to be carried out in many commonly occurring situations in which the customary definitions of residuals fail. Quantile residuals are applied in this article to three example data sets.     

保险动态惩罚机制对网约车平台监督作用的演化博弈研究

采用演化博弈方法,研究保险公司与网约车平台之间的博弈演化过程,分析了在保险公司监督下,网约车平台策略选择的影响因素,并比较了静态惩罚机制和动态惩罚机制下网约车平台与保险公司博弈的均衡策略。研究发现,保险公司的惩罚性保费可以促使网约车平台的策略选择发生改变。在静态惩罚机制下,网约车平台和保险公司的策略选择呈周期波动模式,不能收敛;在动态惩罚机制下,网约车平台和保险公司的博弈呈现螺旋收敛的演化轨迹,且收敛的均衡点不随策略选择的初始概率不同而改变。研究结论明确了保险在网约车行业管理中的社会监督职能,并为保险公司保费的制定提供理论参考。