回归树方法在车险索赔频率预测建模中的应用

近20年来广义线性模型在车险定价领域已成为被广泛使用的标准模型。但随着大数据时代的来临,数据记录变得越来越多,可用于车险定价的解释变量个数也变得越来越多,然而变量间的相关关系却通常很强。在这种情形下,亟待寻找新的定价方法,以实现更为精准的车险定价。本文应用机器学习领域中的回归树方法对车险索赔频率进行了预测建模,研究结果表明回归树方法在车险定价领域是广义线性模型很好的辅助与参考。     

我国车险定价的适当性研究

本文从我国车险定价发展与现状出发,以机动车辆保险的两个基本险定价研究为例,深入分析了目前车险定价中存在的不合理情况,认为我国当前车险定价机制亟待进一步完善,可以通过促进充分竞争、提高精算水平、加强信息披露和具体调整等方面,来进一步完善我国车险的定价机制,从而使车险定价更加科学合理,提高保险公司的竞争力.     

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。     

ZAIG模型在车险定价中的应用研究

近年来,国内财险公司利用广义线性模型（GLMs）对非寿险业务,尤其是车险业务进行建模和精算分析,使得精算技术人员对保险数据的处理更加细致、科学和公平。基于位置、尺度和形状的广义可加模型（GAMLSS）是GLMs、GAMs、DGLMs和GLMMs等的最新拓展,在介绍该模型的定义、算法和模型实现的基础上,以其框架下的零调整逆高斯模型（ZAIG）为一个特例,讨论了其在财险公司财险定价中的应用研究。最后,以瑞士汽车第三者责任保险的一组损失数据为例进行了实证分析,说明了零调整逆高斯模型在车险费率厘定中是一种较合理的方法,为精算技术人员提供参考和借鉴。     

ZAIG模型在车险定价中的应用研究北大核心CSSCI

近年来,国内财险公司利用广义线性模型(GLMs)对非寿险业务,尤其是车险业务进行建模和精算分析,使得精算技术人员对保险数据的处理更加细致、科学和公平。基于位置、尺度和形状的广义可加模型(GAMLSS)是GLMs、GAMs、DGLMs和GLMMs等的最新拓展,在介绍该模型的定义、算法和模型实现的基础上,以其框架下的零调整逆高斯模型(ZAIG)为一个特例,讨论了其在财险公司财险定价中的应用研究。最后,以瑞士汽车第三者责任保险的一组损失数据为例进行了实证分析,说明了零调整逆高斯模型在车险费率厘定中是一种较合理的方法,为精算技术人员提供参考和借鉴。     

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。     

提升算法对传统车险索赔频率建模模型的改进——基于我国五省交强险保单数据

广义线性模型作为非寿险定价的经典模型,在非寿险定价中得到了广泛的应用。近年来,以提升算法为代表的机器学习算法在保险领域取得了很好的效果,为保险产品定价提供了一种新的选择。本文将提升算法思想分别融入到回归树模型和广义线性模型(GLM)中去,用得到的新模型对我国车险索赔频率进行预测建模分析,并与传统的回归树模型和GLM进行比较。结果表明,加入提升算法后传统车险索赔频率建模模型的效果得到了很大的改善,并且在不存在过拟合的前提下,随着模型深度和迭代次数的增加,模型的效果也在不断优化。     

无赔款优待转移概率矩阵测算与应用

无赔款优待（No-Claim Discount,NCD）是最重要的车险定价因子之一。本轮商业车险改革费率方案优化了NCD水平,不同NCD等级的赔付率被进一步拉平,这也使其在以往简单核保规则中的重要性下降。事实上,客户的NCD等级并不是一成不变的,会在下一年出现规律性的迁移。考虑NCD与时间维度的结合,能够为精算与核保定价拓展出一片全新的空间。本文分析了NCD随时间变化的规律,详述了NCD转移概率矩阵的测算过程,并对比了商业车险改革前后其特征变化。通过量化NCD随时间变化的规律,可以为商业车险改革费率方案的可行性提供决策参考,也可成为保险公司优化精算定价与核保规则的有效工具,并为公司开发创新产品提供数据基础。     

非寿险精算中的无赔款优待模型在信用卡年费定价中的运用

虽然国内还没有完全实现银行服务收费的市场化，但银行在服务收费定价方面还有一定的灵活性。国内信用卡业务发展迅速，但银行收取的年费却是单一的，同种类型的信用卡对所有的人都按统一的标准收费。笔者认为，可以尝试引进非寿险精算中的无赔款优待(NCD)模型，加强     

国资划转对企业职工基本养老保险降费空间影响的研究

基于企业职工基本养老保险基金收支精算平衡原理,本文建立企业职工基本养老保险缴费率模型,探讨国资划转对企业职工基本养老保险降费空间的影响。研究发现,国资划转能为养老保险提供降费空间;但当前国资划转比例为养老保险提供的降费空间十分有限;若加大国资划转比例,养老保险降费空间可以提升。进一步研究改变缴费基数对国资划转为养老保险贡献的缴费空间的影响,发现缴费基数增加后,企业平衡缴费率降低,国资划转为养老保险降费率提供的空间减小。本文建议通过提高国有资产划转充实养老保险基金的比例、进行养老保险征管体制改革以做实缴费基数,从而改革和完善企业职工基本养老保险制度。     

投保过程为Poisson过程的一类保险精算模型研究

在传统保险产品定价方法研究基础上,以随机利率为研究前提,对保险公司在一段时间内的投保过程服从Poisson过程的保费收支情况进行了分析,分别讨论了保险公司收入和支出的精算现值,得到保险公司在一段时间内的保费计算模型。     

An Actuarial Premium Pricing Model for Nonnormal Insurance and Financial Risks in Incomplete Markets

Abstract

A model for pricing insurance and financial risks, based on recent developments in actuarial premium principles with elliptical distributions, is developed for application to incomplete markets and heavy-tailed distributions. The pricing model involves an application of a generalized variance premium principle from insurance pricing to the pricing of a portfolio of nontraded risks relative to a portfolio of traded risks. This pricing model for a portfolio of insurance or financial risks reflects preferences for features of the distributions other than mean and variance, including kurtosis. The model reduces to the Capital Asset Pricing Model for multinormal portfolios and to a form of the CAPM in the case where the traded and nontraded risks have the same elliptical distribution.     

Applications of Fuzzy Regression in Actuarial Analysis

In this article, we propose several applications of fuzzy regression techniques for actuarial problems. Our main analysis is motivated, on the one hand, by the fact that several articles in the financial and actuarial literature suggest using fuzzy numbers to model interest rate uncertainty but do not explain how to quantify these rates with fuzzy numbers. Likewise, actuarial literature has recently focused some of its attention in analyzing the Term Structure of Interest Rates (TSIR) because this is a key instrument for pricing insurance contracts. With these two ideas in mind, we show that fuzzy regression is suitable for adjusting the TSIR and discuss how to apply a fuzzy TSIR when pricing life insurance contracts and property‐liability policies. Finally, we reflect on other actuarial applications of fuzzy regression and develop with this technique the London Chain Ladder Method for obtaining Incurred But Not Reported Reserves.     

Fuzzy Financial Pricing of Property-Liability Insurance

Abstract

This paper uses fuzzy set theory (FST) to solve a problem in actuarial science, the financial pricing of property-liability insurance contracts. The fundamental concept of FST is the alternative formalization of membership in a set to include the degree or strength of membership. FST provides consistent mathematical rules for incorporating vague, subjective, or judgmental information into complex decision processes. It is potentially important in insurance pricing because much of the information about cash flows, future economic conditions, risk premiums, and other factors affecting the pricing decision is subjective and thus difficult to quantify by using conventional methods. To illustrate the use of FST, we “fuzzify” a well-known insurance financial pricing model, provide numerical examples of fuzzy pricing, and propose rules for project decision-making using FST. The results indicate that FST can lead to significantly different decisions than the conventional approach.     

动态死亡率下个人年金的长寿风险分析

传统的精算定价方法假定死亡率是静态的,实际上死亡率是随时间而变动的具有动态不确定性的变量。在动态死亡率的框架下定量分析长寿风险对于个人年金产品定价的影响:引入Wang转换的风险定价方法度量长寿风险的市场价格,并运用模拟分析的方法分析长寿风险对个人年金定价的影响。最后,基于分析结果,就保险公司如何管理这一风险给出建议。     

Pricing Double-Trigger Reinsurance Contracts: Financial Versus Actuarial Approach

This article discusses various approaches to pricing double‐trigger reinsurance contracts—a new type of contract that has emerged in the area of ‘‘alternative risk transfer.’’ The potential coverage from this type of contract depends on both underwriting and financial risk. We determine the reinsurer's reservation price if it wants to retain the firm's same safety level after signing the contract, in which case the contract typically must be backed by large amounts of equity capital (if equity capital is the risk management measure to be taken). We contrast the financial insurance pricing models with an actuarial pricing model that has as its objective no lessening of the reinsurance company's expected profits and no worsening of its safety level. We show that actuarial pricing can lead the reinsurer into a trap that results in the failure to close reinsurance contracts that would have a positive net present value because typical actuarial pricing dictates the type of risk management measure that must be taken, namely, the insertion of additional capital. Additionally, this type of pricing structure forces the reinsurance buyer to provide this safety capital as a debtholder. Finally, we discuss conditions leading to a market for double‐trigger reinsurance contracts.     

A general class of distortion operators for pricing contingent claims with applications to CAT bonds

ABSTRACT

The current paper provides a general approach to construct distortion operators that can price financial and insurance risks. Our approach generalizes the (Wang 2000) transform and recovers multiple distortions proposed in the literature as particular cases. This approach enables designing distortions that are consistent with various pricing principles used in finance and insurance such as no-arbitrage models, equilibrium models and actuarial premium calculation principles. Such distortions allow for the incorporation of risk-aversion, distribution features (e.g. skewness and kurtosis) and other considerations that are relevant to price contingent claims. The pricing performance of multiple distortions obtained through our approach is assessed on CAT bonds data. The current paper is the first to provide evidence that jump-diffusion models are appropriate for CAT bonds pricing, and that natural disaster aversion impacts empirical prices. A simpler distortion based on a distribution mixture is finally proposed for CAT bonds pricing to facilitate the implementation.     

Skewed distributions in finance and actuarial science: a review

That the returns on financial assets and insurance claims are not well described by the multivariate normal distribution is generally acknowledged in the literature. This paper presents a review of the use of the skew-normal distribution and its extensions in finance and actuarial science, highlighting known results as well as potential directions for future research. When skewness and kurtosis are present in asset returns, the skew-normal and skew-Student distributions are natural candidates in both theoretical and empirical work. Their parameterization is parsimonious and they are mathematically tractable. In finance, the distributions are interpretable in terms of the efficient markets hypothesis. Furthermore, they lead to theoretical results that are useful for portfolio selection and asset pricing. In actuarial science, the presence of skewness and kurtosis in insurance claims data is the main motivation for using the skew-normal distribution and its extensions. The skew-normal has been used in studies on risk measurement and capital allocation, which are two important research fields in actuarial science. Empirical studies consider the skew-normal distribution because of its flexibility, interpretability, and tractability. This paper comprises four main sections: an overview of skew-normal distributions; a review of skewness in finance, including asset pricing, portfolio selection, time series modeling, and a review of its applications in insurance, in which the use of alternative distribution functions is widespread. The final section summarizes some of the challenges associated with the use of skew-elliptical distributions and points out some directions for future research.     

基于分数维随机利率的分数跳-扩散外汇期权定价

假设利率为分数维随机利率,外汇汇率服从分数跳一扩散过程,并且波动率为常数,期望收益率为时间的非随机函数,本文利用保险精算方法,得出了看涨、看跌外汇欧武期权的一般定价公式,并建立了平价公式。     

Addressing insurance price discrimination in an era of diversity,equity, and inclusion

The early 2020s diversity, equity, and inclusion movement has prompted debate about banning the use of suspect insurance pricing variables because they discriminate against protected classes, such as gender. This paper demonstrates how banning an insurance pricing variable currently used in insurance pricing models can result in regulatory adverse selection if the ban heterogeneously combines policyowners with different expected losses into the same risk class, contrary to risk-based pricing. The paper begins by describing several recent regulatory and judicial decisions to ban insurance pricing variables. It next describes the process used by insurers to set insurance prices, followed by a discussion of applicable insurance discrimination laws. Using a simple risk aversion model, the paper next examines whether a ban on gender-based auto insurance pricing in California in 2019 results in regulatory adverse selection. The paper concludes by describing possible alternative pricing variables available to auto insurers if gender-based pricing is banned.