考虑异常值的改进链梯法

针对传统链梯法评估准备金对异常值的高度敏感性问题,本文提出了一种改进链梯法。直接对增量赔款流量三角形进行分析研究,并引入事故年的逐年进展因子。运用箱线图交叉分析事故年的逐年进展因子表和进展年的逐年进展因子表,确定异常值的位置,然后选择合适插补值代替异常值。数值结果表明：改进链梯法实现了异常值的诊断和修正,并改善了流量三角形对角线异常数据不能被有效识别的情况,优化了链梯法对准备金的估计结果。     

基于操作时间和广义线性混合模型的准备金评估技术研究

基于操作时间来重新设计流量三角形,通过对Hoerl曲线进行推广来刻画异质的损失进展模式,分别建立双广义线性混合模型和Tweedie分布簇广义线性混合模型来评估准备金。该模型可以综合信息平台汇总数据,同时利用个体经验数据和行业数据来评估任何保险公司在任何时点的准备金,解决传统准备金评估技术的弊端,为动态风险监管提供决策依据。在实证分析中,根据重疾险的数据特征,设计适合的准备金评估模型,最后进行对比分析,总结模型方法的优点、缺点和主要结论。     

种植业自然灾害风险模型研究进展

种植业自然灾害风险模型是自然灾害风险定量评估服务于保险精算的重要桥梁,是种植业自然灾害保险公平性与可持续性的重要保障。本文介绍了种植业自然灾害保险精算对风险评估模型的具体需求,回顾并评述了近年来在种植业自然灾害风险模型中的主要进展,总结了四类主要建模方法。对模型发展趋向的研究表明,整合各类建模方法的优势,构建多灾种框架下、灾害事件建模为基础、作物生长模拟为手段的综合模型,准确定量评估各种(次)自然灾害造成的产量损失,有效区分保险责任覆盖的损失与其它损失,实现不同空间尺度的总损失风险估计与转换,是种植业自然灾害风险模型研究的主要方向。进一步开展种植业自然灾害综合风险研究,对构建中国自主知识产权的种植业自然灾害风险模型,以科技促进种植业自然灾害保险专业化发展具有重要意义。     

基于分层动态随机规划的资产负债管理模型

提出一种分层动态随机规划模型,解决资产负债最优配置问题。模型放宽了目标函数必须准确反映投资者收益-风险态度的限制,引入评价指标体系判定最优解。各层次模型考虑了未来市场上的不确定因素,采用动态随机规划基本形式,以情景树作为随机参数输入并得到决策结果。通过对商业银行资产负债配置建模的实例分析验证了该模型的可行性和有效性,使银行在满足流动性和安全性要求的同时,可以获得更高的收益率。     

基于进展时间和操作时间的两步广义线性混合模型非寿险准备金估计

对于非寿险准备金估计,传统流量三角形进展年的选择一直饱受争议,过长时易因数据不足难以估计,过短时可能会出现零赔付的情况。引入操作时间可以解决这一问题,但直接计算的操作时间实际上被严重高估。为此基于信度思想,使用个体信息将保单分组,建立两步广义线性混合模型,首先引入进展时间估计操作时间,再使用操作时间估计指定时间段内的未决赔款准备金。使用某非寿险公司的车损数据进行实证分析,并将该模型与使用传统流量三角的广义线性模型进行对比,结果均表明该模型效果甚佳。     

银行业信用风险宏观压力测试方法研究

三大信用风险模型在国际银行业宏观压力测试实践中被广泛使用,CreditRisk+要求数据较少且计算量较小但难以考虑贷款违约的行业相关性;CreditMetrics很好地考虑了违约行业相关性但要求数据较多且面对较大的贷款组合计算量过大;CreditPortfolioView建模过程中不需额外设计风险传导及情景模型,能直接用于宏观压力测试,但其损失分布计算量较前面2种模型都大。本文为了克服以上不足,在压力情景生成及风险传导部分采用分行业的CPV模型,信用风险计量部分采用违约概率固定的CreditRisk+计算损失分布。该压力测试方法考虑了贷款违约的行业相关性,数据要求较少且计算量小。     

中国地震灾害损失评估：超概率曲线方法与经验数据

我国是地震灾害频发的国家,曾遭受重大的人员伤亡和财产损失。地震灾害损失曲线能够反映地震灾害损失分布情况,对于在事前评估中国地震灾害风险,更好地开展防灾减灾工作有非常重要的意义。本文根据超概率曲线理论,提出一种在有限经验数据的基础上,通过计算机模拟生成长时期大样本的模拟灾害事件,以此构建年度地震灾害损失超概率曲线的方法;并且运用1990年～2011年间中国大陆地区历次地震灾害事件的经验数据,分别建立单起地震灾害损失分布模型和年度成灾地震发生次数分布模型,并通过随机循环抽样模拟生成1 000年的中国地震损失事件,构建出中国年度地震灾害损失超概率曲线。     

基于分层广义线性模型的未决赔款准备金评估方法

本文将分层广义线性模型应用于未决赔款准备金的评估中,充分考虑了保险公司同一事故年赔款数据反复观测的纵向特征和不同事故年未观测到的特征所导致的异质性。从实证结果可以看出,分层广义线性模型可以根据先验信息和经验赔款调整先验权重,并得到与贝叶斯广义线性模型精确度和估计值都非常接近的未决赔款准备金评估值,且在突发事件情景下可以得到更稳定的评估值。     

高龄人口死亡率预测模型的比较与选择

高龄人口死亡率预测模型是人口预测、养老金成本和债务评估以及长寿风险度量与管理的基础。我国大陆地区高龄人口死亡数据量少、数据波动性大,如何选择适合我国高龄数据特点的死亡率预测模型,是重要的研究课题。本文在归纳总结死亡率预测模型研究进展的基础上,先采用数据较为充分的台湾地区高龄死亡数据,选用Lee-Carter、CBD、贝叶斯分层模型等八种死亡率模型,对模型的拟合效果、预测效果和稳健性做出比较。在此基础上,基于修正和平滑后的我国大陆人口死亡数据,采用CBD模型和贝叶斯分层模型建模和预测。结果显示:贝叶斯分层模型能捕捉我国大陆高龄死亡率数据的历史波动,预测区间能够涵盖全部死亡率的真实值,但预测区间过宽,生存曲线不收敛;相比之下,CBD模型对我国大陆地区高龄死亡率的拟合和预测较好,预测区间和生存曲线合理。在长寿风险度量中,建议采用CBD模型。     

XGBoost-Norm模型在信用建模中的分析研究

文章提出一种基于XGBoost的扩展模型XGBoost-Norm,用以解决信用建模中的类别不均衡问题。XGBoost-Norm借鉴了Batch-Normalize机制对每个学习器的输出进行变换,在常用损失函数上进行了多次独立重复试验和试验结果分析。结果显示：XGBoost-Norm模型在常用的损失函数下,AUC显著提升（0.6%）,模型复杂度显著上升;相同AUC指标下,以BCE为损失函数时模型复杂度显著降低。XGBoost-Norm模型能够解决类别不均衡问题,改善模型效果。     

Beyond the Tweedie Reserving Model: The Collective Approach to Loss Development

This article proposes a new loss reserving approach, inspired from the collective model of risk theory. According to the collective paradigm, we do not relate payments to specific claims or policies, but we work within a frequency-severity setting, with a number of payments in every cell of the run-off triangle, together with the corresponding paid amounts. Compared to the Tweedie reserving model, which can be seen as a compound sum with Poisson-distributed number of terms and Gamma-distributed summands, we allow here for more general severity distributions, typically mixture models combining a light-tailed component with a heavier-tailed one, including inflation effects. The severity model is fitted to individual observations and not to aggregated data displayed in run-off triangles with a single value in every cell. In that respect, the modeling approach appears to be a powerful alternative to both the crude traditional aggregated approach based on triangles and the extremely detailed individual reserving approach developing each and every claim separately. A case study based on a motor third-party liability insurance portfolio observed over 2004–2014 is used to illustrate the relevance of the proposed approach.     

Separation of small and large claims on the basis of collective models

This paper is inspired by two papers of Riegel who proposed to consider the paid and incurred loss development of the individual claims and to use a filter in order to separate small and large claims and to construct loss development squares for the paid or incurred small or large claims and for the numbers of large claims. We show that such loss development squares can be constructed from collective models for the accident years. Moreover, under certain assumptions on these collective models, we show that a development pattern exists for each of these loss development squares, which implies that various methods of loss reserving can be used for prediction and that the chain ladder method is a natural method for the prediction of future numbers of large claims.     

Credibility in Loss Reserving

This article proposes using credibility theory in the context of stochastic claims reserving. We consider the situation where an insurer has access to the claims experience of its peer competitors and has the potential to improve prediction of outstanding liabilities by incorporating information from other insurers. Based on the framework of Bayesian linear models, we show that the development factor in the classical chain-ladder setting has a credibility expression: a weighted average of the prior mean and the best estimate from the data. In the empirical analysis, we examine loss triangles for the line of commercial auto insurance from a portfolio of insurers in the United States. We employ hierarchical model for the specification of prior and show that prediction could be improved through borrowing strength among insurers based on a hold-out sample validation.     

Structure and estimation of Lévy subordinated hierarchical Archimedean copulas (LSHAC): Theory and empirical tests

Lévy subordinated hierarchical Archimedean copulas (LSHAC) are flexible models in high dimensional modeling. However, there is limited literature discussing their applications, largely due to the challenges in estimating their structures and their parameters. In this paper, we propose a three-stage estimation procedure to determine the hierarchical structure and the parameters of a LSHAC. This is the first paper to empirically examine the modeling performances of LSHAC models using exchange traded funds. Simulation study demonstrates the reliability and robustness of the proposed estimation method in determining the optimal structure. Empirical analysis further shows that, compared to elliptical copulas, LSHACs have better fitting abilities as well as more accurate out-of-sample Value-at-Risk estimates with less parameters. In addition, from a financial risk management point of view, the LSHACs have the advantage of being very flexible in modeling the asymmetric tail dependence, providing more conservative estimations of the probabilities of extreme downward co-movements in the financial market.     

Factor Copula Approaches for Assessing Spatially Dependent High-Dimensional Risks

In this article, we propose an innovative approach for modeling spatial dependence among losses from various geographical locations. The proposed model converts the challenging task of modeling complex spatial dependence structures into a relatively easier task of estimating a continuous function, of which the arguments can be the coordinates of the locations. The approach is based on factor copula models, which can capture various linear and nonlinear dependence. We use radial basis functions as the kernel smoother for estimating the key function that models all the spatial dependence structures. A case study on a thunderstorm wind loss dataset demonstrates the analysis and the usefulness of the proposed approach. Extensions to spatiotemporal models and to models for discrete data are briefly introduced, with an example given for modeling loss frequency with excess zeros.     

Prediction Error of the Multivariate Chain Ladder Reserving Method

Abstract

In this paper we consider the claims reserving problem in a multivariate context: that is, we study the multivariate chain-ladder (CL) method for a portfolio of N correlated runoff triangles based on multivariate age-to-age factors. This method allows for a simultaneous study of individual runoff subportfolios and facilitates the derivation of an estimator for the mean square error of prediction (MSEP) for the CL predictor of the ultimate claim of the total portfolio. However, unlike the already existing approaches we replace the univariate CL predictors with multivariate ones. These multivariate CL predictors reflect the correlation structure between the subportfolios and are optimal in terms of a classical optimality criterion, which leads to an improvement of the estimator for the MSEP. Moreover, all formulas are easy to implement on a spreadsheet because they are in matrix notation. We illustrate the results by means of an example.     

A simple non-linear model with fractional integration for financial time series data

This paper provides several examples of simple non-linear time series models with fractionally integrated disturbances. Both types of models (non-linear and fractional integration) have been widely used in recent years when modeling financial data. We use a testing procedure that permits us to test the order of integration in raw time series in the context of non-linear models. The tests are applied to several financial time series, the results showing that when the non-linear sign structure is taken into account, the order of integration of the series is much higher than one, finding thus conclusive evidence against mean reversion in their behavior.     

Lognormal Mixed Models for Reported Claims Reserves

Abstract

Traditional claims-reserving techniques are based on so-called run-off triangles containing aggregate claim figures. Such a triangle provides a summary of an underlying data set with individual claim figures. This contribution explores the interpretation of the available individual data in the framework of longitudinal data analysis. Making use of the theory of linear mixed models, a flexible model for loss reserving is built. Whereas traditional claims-reserving techniques don’t lead directly to predictions for individual claims, the mixed model enables such predictions on a sound statistical basis with, for example, confidence regions. Both a likelihood-based as well as a Bayesian approach are considered. In the frequentist approach, expressions for the mean squared error of prediction of an individual claim reserve, origin year reserves, and the total reserve are derived. Using MCMC techniques, the Bayesian approach allows simulation from the complete predictive distribution of the reserves and the calculation of various risk measures. The paper ends with an illustration of the suggested techniques on a data set from practice, consisting of Belgian automotive third-party liability claims. The results for the mixed-model analysis are compared with those obtained from traditional claims-reserving techniques for run-off triangles. For the data under consideration, the lognormal mixed model fits the observed individual data well. It leads to individual predictions comparable to those obtained by applying chain-ladder development factors to individual data. Concerning the predictive power on the aggregate level, the mixed model leads to reasonable predictions and performs comparable to and often better than the stochastic chain ladder for aggregate data.     

“The Future of Risk Classification in the Age of Predictive DNA-Based Testing”, Donald C. Chambers,January 1999

Abstract

The correlation among multiple lines of business plays an important role in quantifying the uncertainty of loss reserves for insurance portfolios. To accommodate correlation, most multivariate loss-reserving methods focus on the pairwise association between corresponding cells in multiple run-off triangles. However, such practice usually relies on the independence assumption across accident years and ignores the calendar year effects that could affect all open claims simultaneously and induce dependencies among loss triangles. To address this issue, we study a Bayesian log-normal model in the prediction of outstanding claims for dependent lines of business. In addition to the pairwise correlation, our method allows for an explicit examination of the correlation due to common calendar year effects. Further, different specifications of the calendar year trend are considered to reflect valuation actuaries’ prior knowledge of claim development. In a case study, we analyze an insurance portfolio of personal and commercial auto lines from a major U.S. property-casualty insurer. It is shown that the incorporation of calendar year effects improves model fit significantly, though it contributes substantively to the predictive variability. The availability of the realizations of predicted claims permits us to perform a retrospective test, which suggests that extra prediction uncertainty is indispensable in modern risk management practices.     

Yield-factor volatility models

The term structure of interest rates is often summarized using a handful of yield factors that capture shifts in the shape of the yield curve. In this paper, we develop a comprehensive model for volatility dynamics in the level, slope, and curvature of the yield curve that simultaneously includes level and GARCH effects along with regime shifts. We show that the level of the short rate is useful in modeling the volatility of the three yield factors and that there are significant GARCH effects present even after including a level effect. Further, we find that allowing for regime shifts in the factor volatilities dramatically improves the model’s fit and strengthens the level effect. We also show that a regime-switching model with level and GARCH effects provides the best out-of-sample forecasting performance of yield volatility. We argue that the auxiliary models often used to estimate term structure models with simulation-based estimation techniques should be consistent with the main features of the yield curve that are identified by our model.