基于行为博弈的机动车辆保险奖惩系统的研究
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摘要
自20世纪初期以来,伴随着汽车的发明及推广应用,机动车辆保险也经历了一个从无到有、快速发展的过程,已成为经济社会中最为重要的险种之一。车险业务经营效益的好环将直接关系到财险公司的成败。保费是保险企业的生产过程或生产增值链中必备的现金流入,相应地,保费制度成为保证保险企业的偿付能力的关键要素。奖惩系统(Bonus-Malus System,BMS)作为经验费率制度的应用分支,是车险费率制度中不可或缺的组成部分,又是反映投保人和保险人之间的保险交易关系的重要载体。精算师在实践中已总结出构造最优BMS的一整套方法,但忽略了投保人在BMS条件下的行为偏好及其对BMS运作的潜在影响。出于上述考虑,本文突破已有的BMS研究的精算框架,从投保人和保险人之间行为博弈的视角全新梳理车险奖惩制度,在寻求精算学和经济学的嫁接思路的同时,试图为我国机动车辆保险的实践提供理论启示。
围绕研究意图,本文首先在文献综述的基础上,确立起行为博弈的分析视角;解析费率分级机制的两个层面:先验分级和BMS,重点归纳国际上BMS的运作模式,并附以对我国车险费率分级效率的评价;以实践认识为铺垫,依托经济学理论解释和论证BMS介入车险业务的合理性。至此,着手讨论需要解决的相关问题。出于优化交易利益的考虑,探讨先验分级和奖惩系统的整合运作问题;着重分析BMS框架下投保人可能表现出的信息不对称问题(动态道德风险和奖金饥渴症),并给出相应的治理思路。按照上述的行文思路,各章研究得出的主要结论如下:
第1章综述了国内外BMS研究的文献,指出纯精算角度研究BMS存在的缺陷,即忽略了投保人的行为偏好可能带给BMS精算的变化风险。为此,提出运用行为博弈的分析方法来协调投保人和保险人之间的交易关系,在此基础上给出本文需要解决的问题。
第2章归纳了车险费率分级机制的两个层面的实践经验,实证考察我国的车险费率分级操作,分析表明先验分级效率不高,BMS在奖惩力度、费率差异化等方面存有不足,但具备快速收敛于稳态概率分布的能力。
第3章运用经济学理论系统评价经验估费制度。依据静态福利分析,BMS不能改进固定保险范围的强制车险的市场效率,而对于可变保险范围的商业车险能起到优化保险市场资源配置效率的作用。此外,BMS对于信息不对称条件下投保人可能表现出来的逆向选择、道德风险和保险欺诈等机会主义行为具有抑制作用。因此,在车险业务中引入BMS具有很好的实践意义。
第4章探讨车险费率分级机制的两个层面如何整合运作的问题。首先,从理论上揭示出两者之间应有着交替、互斥的关系;其次,说明现有的最优BMS精算模型存在的问题,即割裂了两个层面的内在联系,造成投保人面临双重惩罚或奖励的可能;由此,提出一个整合先验分级和BMS的保险定价模型,使得BMS仅针对先验分级后残余的风险异质性区分初始保费;最后,基于实际数据对比两类精算模型,验证了整合效果。
第5章讨论BMS条件下动态道德风险的两种表现形式:出险依赖效应和合约时间效应,并给出动态道德风险的规范策略。当保费仅占投保人的收入的极小比重时,出险依赖效应成立。即存在道德风险时,随着事故的边际成本递增(即续期保费增加),投保人的驾车行为会更加谨慎。非参数假设检验揭示出我国车险市场上存在合约时间效应。即在动态激励条件下投保人的行为偏好呈现出非平稳性的特点,越是临近保险契约的调整时点,驾车行为越趋于谨慎。
第6章研究奖金饥渴症的产生根源及其治理机制。奖金饥渴症表现为投保人为了获得优惠费率而自担小额损失。奖金饥渴症截断投保人的真实损失分布,增大了保险人的定价风险,并会使BMS陷入财务失衡的困境。BMS条件下投保人的索赔策略可看作自留损失和保险索赔的融资成本比较的结果。奖金饥渴症的成形基础是保险索赔的融资成本高于自留损失的融资成本。设置合理的契约免赔额和优化BMS奖惩幅度都是降低BMS条件保险索赔的融资成本的可行途径,进而对奖金饥渴症起到抑制效果。
第7章总结本文的研究工作,联系我国车险业务的实践状况,给出具体的启示或建议,最后指出本文研究的不足和后续研究的方向。
本文的主要创新之处如下:
1.改进Chiappori & Salanié(2000)的计量模型,构建多元Probit模型评价车险先验分级的效率,结合我国车险业务的保单数据开展实证分析。一方面,多元Probit模型可以对先验分级变量的分级效果作出统计检验,对于筛选适宜的先验分级变量、定义分级变量的取值类别都有一定的指导作用:另一方面,借助于判断先验分级之后车险业务中是否残存逆向选择,多元Probit模型对先验分级效率的全局评价显得更加稳健,实证分析的结果验证了这一点。
2.纠正现有的最优BMS精算模型的缺陷,提出整合先验分级的BMS精算模型。理论分析表明,先验分级和BMS应表现为交替、互斥的关系。现有的最优BMS精算模型是基于保单组合的风险异质性而不是先验分级后残余的风险异质性来推算奖惩系数,不可避免地对投保人实施了双重惩罚或者奖励;而整合先验分级的BMS精算模型仅以残余的风险异质性为基准调整初始保费,实证研究证实改进模型起到了理顺两个分级环节的运作关系的效果。
3.梳理动态道德风险的两种表现形式:出险依赖效应和合约时间效应,并给出各自的规范策略。构建博弈分析模型,讨论保费水平的变动与投保人谨慎程度的投入之间的关系,表明BMS框架下存在出险依赖效应,即出险概率与索赔成本之间有着负向联系。递增的免赔额体系可用于强化出险依赖效应,使得投保人的风险属性相对稳定。设计非参数假设检验方法,揭示出我国车险市场上存在着合约时间效应。并且,对保险期和考察期进行错位安排是缓和合约时间效应的可行思路。
4.结合奖金饥渴症的产生根源,归纳奖金饥渴症的治理思路:确定最优契约免赔额和优化BMS的奖惩幅度。两种治理思路具有相同的出发点,即控制保险赔付的损失融资成本,使得投保人自担损失的融资成本尽可能地高于保险赔付的损失融资成本,以此削弱奖金饥渴症产生的根基。具体来看,契约免赔额d和投保人的自担免赔额z(d)之间满足z′(d)=-1时达最优;而基于指数损失函数厘定的BMS系数有助于优化设置等级保费之间的奖惩幅度。
Since the early days of the twentieth century, motor insurance has experienced an emerging and surging process of development along with the invention and popularization of automobile, becoming one of the important policies in the social economy. Whether a property insurance company can be successful or not, which rests with the performance of the motor insurance line. As premium represents essential cash flow for the operating process or value-added chain of the insurance company, premium scheme is the key element to ensure its solvency. Being an applied branch of experience rating, Bonus-Malus system (BMS) is an indispensable component to the premium scheme of motor insurance, which also is an important carrier to reflect the transaction relationship between the insured and the insurer. In practice, actuaries have summarized a set of methodologies to construct the optimal BMS, but they don't take into account the behavioral performance of the insured and its impact on the operation of BMS. Based on the above consideration, the paper breaks through the existed framework to study BMS, while reviewing it from a new angle upon the behavioral game between the two parties. The paper attempts to provide theoretical directions for the practice of Chinese motor insurance industry, meanwhile seeking out proper ways to graft economics to actuarial science.
Following the research purpose, firstly the paper summarizes the relative literatures, to establish the analytical perspective of behavioral game. Decomposing the premium classification mechanism into two layers (i.e. ex ante classification and BMS), it pays special attention to conclude the operating modes of BMS internationally, combined with assessing the premium classification efficiency of Chinese motor insurance. Backed with the full acquaintance of BMS practice, it relies on economics to verify the rationality of introducing BMS into motor insurance. Thus, the paper comes to discuss certain problems need to be settled. In order to optimize the transaction interests, it probes into the problem how to integrate ex ante classification with BMS. It gives prominence to analyze the asymmetric information problems (i.e. dynamic moral hazard and hunger for bonus) the policyholder may display under the BMS setting, furthermore, the governance strategies are put forward correspondingly. According to the study plan, the main conclusions drawn from the chapters are as follows:
Chapter 1 sums up the domestic and abroad literatures on BMS, points out the limitation of BMS study from the angle of actuarial science purely, that is, ignoring the policyholder's behavioral preference and arousing change risks to BMS pricing. Therefore, it suggests to use behavioral game to coordinate the transaction relationship between the insured and the insurer, the problems to be tackled are brought forward subsequently.
Chapter 2 concludes the practical experience for the two layers of the premium classification mechanism, evaluates the practice of premium classification in Chinese motor insurance market. It shows that ex ante classification is lack of efficiency. BMS has deficiencies in certain aspects such as the span between bonus and malus, premium differentiation etc., although it is of the ability to converge to stationary probability distribution quickly.
Chapter 3 assesses experience rating scheme systematically relying on economics theories. According to static welfare analysis, BMS can't improve the market efficiency for statutory motor insurance with fixed coverage, while it plays a role to optimize the resource-allocating efficiency of insurance market for commercial motor insurance with variable coverage. Otherwise, BMS can restrain the opportunism behavior that policyholders may reveal under the circumstances of asymmetric information. In this case, it is of practical significance to introduce BMS into motor insurance business.
Chapter 4 investigates the problem how to integrate the two layers of the premium classification mechanism. Firstly, it indicates that there exists substitutive and repulsive relationship between the two layers in theory. Secondly, it explains the limitation that the current actuarial model of the optimal BMS has, that is, segmenting the inherent linkage between the two layers, which results in the possibility that the policyholder confronts dual punishment or reward. Then, an insurance pricing model integrated ex ant classification with BMS is set up, which follows the idea that the degree of BMS differentiating base premium is only aimed to the residual risk heterogeneity after ex ant classification. Finally, a comparison between the former model and the integrated one is carried out on the basis of actual data, which validate the hypothetic effects on integration.
Chapter 5 discusses the two representations of dynamic moral hazard under the circumstances of BMS, i.e. occurrence dependence effect and contract-time one, and governance strategies on dynamic moral hazard are provided. When premium just accounts for a tiny proportion to the policyholder's income, occurrence dependence effect comes into existence. That is, if moral hazard does exist, along with the increasing of the marginal cost for an accident, the policyholder's driving behavior becomes more cautious. It finds that there exists contract-time effect in Chinese motor insurance market by non-parameter hypothesis testing. That is, the policyholder's behavioral preference isn't stationary under dynamic incentive situations. The more near to the adjusting time of insurance contract, the more cautious the policyholder's driving behavior shows.
Chapter 6 studies the origin of hunger for bonus and the corresponding governance strategies. Hunger for bonus is a behavioral tendency that the policyholder bears small losses to obtain favorable renewal premium. It is obvious that hunger for bonus truncate the policyholder's true loss distribution, which increases the pricing risks the insurer faces and gets BMS into the puzzledom of financial disbalance. Under the framework of BMS, the policyholder's claim strategy can be regarded as choosing a preferable means of loss financing by comparing financing costs between retention and claim. Therefore, the foundation of hunger for bonus is that the financing cost corresponding to claim is greater than that corresponding to retention. As setting proper contractual deductible and optimizing the bonus-malus scales are feasible routes to reduce the financing cost corresponding to claim under the framework of BMS, they both exert restrainable effects on hunger for bonus.
Chapter 7 summarizes the whole research of the paper. Focusing on the practical status of Chinese motor insurance, it come out some revelations or suggestions, the deficiencies and further research directions being put forward together.
The main innovations of the paper are as follows:
1. Through modifying the econometric model established by Chiappori & Salanie (2000), it constructs a multivariable Probit model to evaluate the efficiency of ex ant classification in motor insurance, attached with an empirical analysis using Chinese policy data. On the one hand, multivariable Probit model can be used to test the differentiating effect of a classifying variable, so it has certain directions to screen proper ex ant classifying variable and define its value space. On the other hand, relying on judging whether there exists residual adverse selection or not among motor insurance business, the overall evaluation on the efficiency of ex ant classification obtained by multivariable Probit model seems to be more reliable, which is verified by the empirical analysis.
2. To rectify the defect involved in the current actuarial model of the optimal BMS, it brings forward a BMS actuarial model integrated with ex ant classification. Theoretical analysis shows that the relationship between ex ant classification and BMS should be a substitutive and repulsive one. The current actuarial model of the optimal BMS is based on the risk heterogeneity among the portfolio to calculate bonus-malus coefficients rather than the residual risk heterogeneity after ex ant classification, so it is inevitable to implement dual punishment or reward to the policyholders. However, the BMS actuarial model adjusts the base premium just on the residual heterogeneity. Empirical analysis proves that the new model does improve the relationship between the two layers.
3. Summarizing the two representations, i.e. occurrence dependence effect and contract-time one, it also provides corresponding governance strategies. Through constructing a game model, it discusses the relationship between the premium variation and the cautiousness the policyholder exerts, and reflects that there exists occurrence dependence under the framework of BMS, that is, there is negative relationship between occurrence probability and claim cost. Ascending deductible scheme is suggested to consolidate occurrence dependence effect, for purpose of stabilizing the policyholder's risk attribute. By designing a non-parameter hypothesis testing, it discloses that there is contract-time effect in Chinese motor insurance market. Furthermore, staggering the coverage period and the recording one is a credible way to alleviate contract-time effect.
4. Combined with analyzing the origin of hunger for bonus, it concludes its governance means, i.e. setting proper contractual deductible and optimizing the bonus-malus scales. The two governance means share the same idea that controlling the loss financing cost corresponding to claim, and make the relative cost corresponding to retention is greater than that corresponding to claim, in order toweaken the foundation of hunger for bonus. Properly speaking, only when contractual deductible(d) and the policyholder's retentive deductible z(d) satisfy z'(d) = -1,contractual deductible reaches optimization. As for optimizing the bonus-malus scales, it should rely on exponential loss function to get bonus-malus coefficients.
围绕研究意图,本文首先在文献综述的基础上,确立起行为博弈的分析视角;解析费率分级机制的两个层面:先验分级和BMS,重点归纳国际上BMS的运作模式,并附以对我国车险费率分级效率的评价;以实践认识为铺垫,依托经济学理论解释和论证BMS介入车险业务的合理性。至此,着手讨论需要解决的相关问题。出于优化交易利益的考虑,探讨先验分级和奖惩系统的整合运作问题;着重分析BMS框架下投保人可能表现出的信息不对称问题(动态道德风险和奖金饥渴症),并给出相应的治理思路。按照上述的行文思路,各章研究得出的主要结论如下:
第1章综述了国内外BMS研究的文献,指出纯精算角度研究BMS存在的缺陷,即忽略了投保人的行为偏好可能带给BMS精算的变化风险。为此,提出运用行为博弈的分析方法来协调投保人和保险人之间的交易关系,在此基础上给出本文需要解决的问题。
第2章归纳了车险费率分级机制的两个层面的实践经验,实证考察我国的车险费率分级操作,分析表明先验分级效率不高,BMS在奖惩力度、费率差异化等方面存有不足,但具备快速收敛于稳态概率分布的能力。
第3章运用经济学理论系统评价经验估费制度。依据静态福利分析,BMS不能改进固定保险范围的强制车险的市场效率,而对于可变保险范围的商业车险能起到优化保险市场资源配置效率的作用。此外,BMS对于信息不对称条件下投保人可能表现出来的逆向选择、道德风险和保险欺诈等机会主义行为具有抑制作用。因此,在车险业务中引入BMS具有很好的实践意义。
第4章探讨车险费率分级机制的两个层面如何整合运作的问题。首先,从理论上揭示出两者之间应有着交替、互斥的关系;其次,说明现有的最优BMS精算模型存在的问题,即割裂了两个层面的内在联系,造成投保人面临双重惩罚或奖励的可能;由此,提出一个整合先验分级和BMS的保险定价模型,使得BMS仅针对先验分级后残余的风险异质性区分初始保费;最后,基于实际数据对比两类精算模型,验证了整合效果。
第5章讨论BMS条件下动态道德风险的两种表现形式:出险依赖效应和合约时间效应,并给出动态道德风险的规范策略。当保费仅占投保人的收入的极小比重时,出险依赖效应成立。即存在道德风险时,随着事故的边际成本递增(即续期保费增加),投保人的驾车行为会更加谨慎。非参数假设检验揭示出我国车险市场上存在合约时间效应。即在动态激励条件下投保人的行为偏好呈现出非平稳性的特点,越是临近保险契约的调整时点,驾车行为越趋于谨慎。
第6章研究奖金饥渴症的产生根源及其治理机制。奖金饥渴症表现为投保人为了获得优惠费率而自担小额损失。奖金饥渴症截断投保人的真实损失分布,增大了保险人的定价风险,并会使BMS陷入财务失衡的困境。BMS条件下投保人的索赔策略可看作自留损失和保险索赔的融资成本比较的结果。奖金饥渴症的成形基础是保险索赔的融资成本高于自留损失的融资成本。设置合理的契约免赔额和优化BMS奖惩幅度都是降低BMS条件保险索赔的融资成本的可行途径,进而对奖金饥渴症起到抑制效果。
第7章总结本文的研究工作,联系我国车险业务的实践状况,给出具体的启示或建议,最后指出本文研究的不足和后续研究的方向。
本文的主要创新之处如下:
1.改进Chiappori & Salanié(2000)的计量模型,构建多元Probit模型评价车险先验分级的效率,结合我国车险业务的保单数据开展实证分析。一方面,多元Probit模型可以对先验分级变量的分级效果作出统计检验,对于筛选适宜的先验分级变量、定义分级变量的取值类别都有一定的指导作用:另一方面,借助于判断先验分级之后车险业务中是否残存逆向选择,多元Probit模型对先验分级效率的全局评价显得更加稳健,实证分析的结果验证了这一点。
2.纠正现有的最优BMS精算模型的缺陷,提出整合先验分级的BMS精算模型。理论分析表明,先验分级和BMS应表现为交替、互斥的关系。现有的最优BMS精算模型是基于保单组合的风险异质性而不是先验分级后残余的风险异质性来推算奖惩系数,不可避免地对投保人实施了双重惩罚或者奖励;而整合先验分级的BMS精算模型仅以残余的风险异质性为基准调整初始保费,实证研究证实改进模型起到了理顺两个分级环节的运作关系的效果。
3.梳理动态道德风险的两种表现形式:出险依赖效应和合约时间效应,并给出各自的规范策略。构建博弈分析模型,讨论保费水平的变动与投保人谨慎程度的投入之间的关系,表明BMS框架下存在出险依赖效应,即出险概率与索赔成本之间有着负向联系。递增的免赔额体系可用于强化出险依赖效应,使得投保人的风险属性相对稳定。设计非参数假设检验方法,揭示出我国车险市场上存在着合约时间效应。并且,对保险期和考察期进行错位安排是缓和合约时间效应的可行思路。
4.结合奖金饥渴症的产生根源,归纳奖金饥渴症的治理思路:确定最优契约免赔额和优化BMS的奖惩幅度。两种治理思路具有相同的出发点,即控制保险赔付的损失融资成本,使得投保人自担损失的融资成本尽可能地高于保险赔付的损失融资成本,以此削弱奖金饥渴症产生的根基。具体来看,契约免赔额d和投保人的自担免赔额z(d)之间满足z′(d)=-1时达最优;而基于指数损失函数厘定的BMS系数有助于优化设置等级保费之间的奖惩幅度。
Since the early days of the twentieth century, motor insurance has experienced an emerging and surging process of development along with the invention and popularization of automobile, becoming one of the important policies in the social economy. Whether a property insurance company can be successful or not, which rests with the performance of the motor insurance line. As premium represents essential cash flow for the operating process or value-added chain of the insurance company, premium scheme is the key element to ensure its solvency. Being an applied branch of experience rating, Bonus-Malus system (BMS) is an indispensable component to the premium scheme of motor insurance, which also is an important carrier to reflect the transaction relationship between the insured and the insurer. In practice, actuaries have summarized a set of methodologies to construct the optimal BMS, but they don't take into account the behavioral performance of the insured and its impact on the operation of BMS. Based on the above consideration, the paper breaks through the existed framework to study BMS, while reviewing it from a new angle upon the behavioral game between the two parties. The paper attempts to provide theoretical directions for the practice of Chinese motor insurance industry, meanwhile seeking out proper ways to graft economics to actuarial science.
Following the research purpose, firstly the paper summarizes the relative literatures, to establish the analytical perspective of behavioral game. Decomposing the premium classification mechanism into two layers (i.e. ex ante classification and BMS), it pays special attention to conclude the operating modes of BMS internationally, combined with assessing the premium classification efficiency of Chinese motor insurance. Backed with the full acquaintance of BMS practice, it relies on economics to verify the rationality of introducing BMS into motor insurance. Thus, the paper comes to discuss certain problems need to be settled. In order to optimize the transaction interests, it probes into the problem how to integrate ex ante classification with BMS. It gives prominence to analyze the asymmetric information problems (i.e. dynamic moral hazard and hunger for bonus) the policyholder may display under the BMS setting, furthermore, the governance strategies are put forward correspondingly. According to the study plan, the main conclusions drawn from the chapters are as follows:
Chapter 1 sums up the domestic and abroad literatures on BMS, points out the limitation of BMS study from the angle of actuarial science purely, that is, ignoring the policyholder's behavioral preference and arousing change risks to BMS pricing. Therefore, it suggests to use behavioral game to coordinate the transaction relationship between the insured and the insurer, the problems to be tackled are brought forward subsequently.
Chapter 2 concludes the practical experience for the two layers of the premium classification mechanism, evaluates the practice of premium classification in Chinese motor insurance market. It shows that ex ante classification is lack of efficiency. BMS has deficiencies in certain aspects such as the span between bonus and malus, premium differentiation etc., although it is of the ability to converge to stationary probability distribution quickly.
Chapter 3 assesses experience rating scheme systematically relying on economics theories. According to static welfare analysis, BMS can't improve the market efficiency for statutory motor insurance with fixed coverage, while it plays a role to optimize the resource-allocating efficiency of insurance market for commercial motor insurance with variable coverage. Otherwise, BMS can restrain the opportunism behavior that policyholders may reveal under the circumstances of asymmetric information. In this case, it is of practical significance to introduce BMS into motor insurance business.
Chapter 4 investigates the problem how to integrate the two layers of the premium classification mechanism. Firstly, it indicates that there exists substitutive and repulsive relationship between the two layers in theory. Secondly, it explains the limitation that the current actuarial model of the optimal BMS has, that is, segmenting the inherent linkage between the two layers, which results in the possibility that the policyholder confronts dual punishment or reward. Then, an insurance pricing model integrated ex ant classification with BMS is set up, which follows the idea that the degree of BMS differentiating base premium is only aimed to the residual risk heterogeneity after ex ant classification. Finally, a comparison between the former model and the integrated one is carried out on the basis of actual data, which validate the hypothetic effects on integration.
Chapter 5 discusses the two representations of dynamic moral hazard under the circumstances of BMS, i.e. occurrence dependence effect and contract-time one, and governance strategies on dynamic moral hazard are provided. When premium just accounts for a tiny proportion to the policyholder's income, occurrence dependence effect comes into existence. That is, if moral hazard does exist, along with the increasing of the marginal cost for an accident, the policyholder's driving behavior becomes more cautious. It finds that there exists contract-time effect in Chinese motor insurance market by non-parameter hypothesis testing. That is, the policyholder's behavioral preference isn't stationary under dynamic incentive situations. The more near to the adjusting time of insurance contract, the more cautious the policyholder's driving behavior shows.
Chapter 6 studies the origin of hunger for bonus and the corresponding governance strategies. Hunger for bonus is a behavioral tendency that the policyholder bears small losses to obtain favorable renewal premium. It is obvious that hunger for bonus truncate the policyholder's true loss distribution, which increases the pricing risks the insurer faces and gets BMS into the puzzledom of financial disbalance. Under the framework of BMS, the policyholder's claim strategy can be regarded as choosing a preferable means of loss financing by comparing financing costs between retention and claim. Therefore, the foundation of hunger for bonus is that the financing cost corresponding to claim is greater than that corresponding to retention. As setting proper contractual deductible and optimizing the bonus-malus scales are feasible routes to reduce the financing cost corresponding to claim under the framework of BMS, they both exert restrainable effects on hunger for bonus.
Chapter 7 summarizes the whole research of the paper. Focusing on the practical status of Chinese motor insurance, it come out some revelations or suggestions, the deficiencies and further research directions being put forward together.
The main innovations of the paper are as follows:
1. Through modifying the econometric model established by Chiappori & Salanie (2000), it constructs a multivariable Probit model to evaluate the efficiency of ex ant classification in motor insurance, attached with an empirical analysis using Chinese policy data. On the one hand, multivariable Probit model can be used to test the differentiating effect of a classifying variable, so it has certain directions to screen proper ex ant classifying variable and define its value space. On the other hand, relying on judging whether there exists residual adverse selection or not among motor insurance business, the overall evaluation on the efficiency of ex ant classification obtained by multivariable Probit model seems to be more reliable, which is verified by the empirical analysis.
2. To rectify the defect involved in the current actuarial model of the optimal BMS, it brings forward a BMS actuarial model integrated with ex ant classification. Theoretical analysis shows that the relationship between ex ant classification and BMS should be a substitutive and repulsive one. The current actuarial model of the optimal BMS is based on the risk heterogeneity among the portfolio to calculate bonus-malus coefficients rather than the residual risk heterogeneity after ex ant classification, so it is inevitable to implement dual punishment or reward to the policyholders. However, the BMS actuarial model adjusts the base premium just on the residual heterogeneity. Empirical analysis proves that the new model does improve the relationship between the two layers.
3. Summarizing the two representations, i.e. occurrence dependence effect and contract-time one, it also provides corresponding governance strategies. Through constructing a game model, it discusses the relationship between the premium variation and the cautiousness the policyholder exerts, and reflects that there exists occurrence dependence under the framework of BMS, that is, there is negative relationship between occurrence probability and claim cost. Ascending deductible scheme is suggested to consolidate occurrence dependence effect, for purpose of stabilizing the policyholder's risk attribute. By designing a non-parameter hypothesis testing, it discloses that there is contract-time effect in Chinese motor insurance market. Furthermore, staggering the coverage period and the recording one is a credible way to alleviate contract-time effect.
4. Combined with analyzing the origin of hunger for bonus, it concludes its governance means, i.e. setting proper contractual deductible and optimizing the bonus-malus scales. The two governance means share the same idea that controlling the loss financing cost corresponding to claim, and make the relative cost corresponding to retention is greater than that corresponding to claim, in order toweaken the foundation of hunger for bonus. Properly speaking, only when contractual deductible(d) and the policyholder's retentive deductible z(d) satisfy z'(d) = -1,contractual deductible reaches optimization. As for optimizing the bonus-malus scales, it should rely on exponential loss function to get bonus-malus coefficients.
引文
[1]数据摘自《2006年国民经济和社会发展统计公报》,其中包括三轮汽车和低速货车1399万辆。
[1]需要说明的是,充分费率一般不等同于保险产品价格,虽然后者建立在前者的基础之上,但市场经济条件下的保险业务中,充分费率仅仅反映了保险人的保费要求,实际保险价格的订立还需兼顾市场竞争环境、顾客出价能力、营销发行体系等多方因素。
[2][德]D.法尼.保险企业管理学[M].张庆洪,陆新等译.北京:经济科学出版社,2002.pp 33.
[1]独立同分布是中心极限定理和辛钦大数定律成立的必要条件。中心极限定理阐明了即使原来并不服从正态分布的独立同分布的随机变量,它们的总和(或者均值)的分布渐近地服从正态分布;辛钦大数定律表明大量的独立同分布的随机变量依概率收敛于平均值。它们都揭示出大样本具有稳定性的规律,成为保险业务赖于存在的数理基础。
[2]这里有几个术语需要稍作区别。经验费率(experience rating),或称为费率增减法(merit rating),是依据被保险人过去的实际损失经验调整其初始保费的做法,一般以过去若干年的平均赔付为基础来浮动费率,以反映保险标的的差异性。车险中普遍采用的奖惩系统或者无赔款优待系统是经验费率的特例,两者都是依据理赔次数而不是理赔金额来调整初始保费;相比之下,奖惩系统的费率浮动幅度比无赔款优待系统大得多,前者实行奖优罚劣的双向浮动,而后者只实行单向减费浮动,即不发生赔付时享受费率折扣,而发生赔付时维持原有费率不变。在我国,尽管车险费率浮动机制早已实现了从无赔款优待系统到奖惩系统的升级,但是由于“无赔款优待”概念引入我国的时间较长,社会认同度较高,当前的车险条款仍沿用“无赔款优待”概念表述“奖惩系统”。
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[2]这篇论文的第1作者和第2作者分别是中国人民大学的孟生旺教授和袁卫教授。
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[1]目前为止,韩国被认为是世界上唯一采用考虑索赔大小的BMS的国家(崔树贤和邵学清,2006)。
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[1]Loimaranta(1972)根据马尔可夫链的性质,指出当奖励系统满足以下条件时:(1)特定保单在单个保险期内的索赔次数的概率分布与具体的保险期无关(即是时齐的),(2)无索赔概率p_0(λ)＞0,概率转移矩阵存在稳定状态,那么马尔可夫链是遍历的。
[1]奖惩系统被认为具有激励投保人谨慎行车的作用,这样索赔次数表现出负传染性(ncgative contagion),即前期报告索赔的投保人今后发生索赔的可能性小于未报告索赔的投保人。当然,还有一种主流观点认为汽车保险的承保风险是外生的(exogenous),所以索赔事故具有正传染性(positive contagion)。
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[1]与超额收费相对应的是不足收费(undercharge),但超额收费更受关注。从管理者的角度看,对超额收费和不足收费不应该一视同仁,向投保人超额收费比不足收费要严重得多(Lemaire,1995)。实际上,财务稳定的奖惩系统在对高风险投保人超额收费的同时,必然在对低风险投保人不足收费。因此,消除超额收费或不足收费是实现BMS“费用再分配的合理性”这一相同目标的不同路径。
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[1]该篇论文的第1作者和第2作者分别是中国人民大学的肖宇谷博士和孟生旺教授。
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[1]关于“合约时间效应”的具体说明参见本文第25页。
[2]克里斯汀·蒙特和丹尼尔·塞拉(2005)对“博弈”和“决策”作了区别。博弈论(又称对策论)足分析多个参与者之间相互影响时策略的均衡问题,而决策论是讨论单一参与者最优策略的选择问题。决策论也可以视为一种特殊的双人博弈,只不过其中一方是一个虚拟的参与者——“自然”,另一方的效用由他(她)的决策和自然状态共同决定。因此,两者的区别:决策问题中的不确定性只来源于“自然”的随机步,博弈问题中的不确定性是由于对手策略的预期是外生的。
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[1]从狭义上讲,保险欺诈专指投保人利用不正当手段谋取保险金的行为,具体表现为虚构保险标的、编造保险事故、跨大损失程度等。从广义上来看,保险欺诈的发起人不仅包括投保人,还可能包括保险人、保险中介人,如保险人以不合理的保险条款和费率承保业务,保险代理人误导投保人、私吞保费、造假赔案等(边文霞,2006)。归结起来,保险欺诈是泛指欺诈者利用保险谋求不当利益的行为。考虑到BMS的受用者仅为投保人,本文研究采纳狭义的保险欺诈概念。
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[1]首次索赔决定了保费调整的方向(奖励或惩罚),较之后续索赔对于投保人的影响更大,因此首次索赔时点更能反映投保人在BMS条件下的行为偏好。
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[1]需要说明的是,充分费率一般不等同于保险产品价格,虽然后者建立在前者的基础之上,但市场经济条件下的保险业务中,充分费率仅仅反映了保险人的保费要求,实际保险价格的订立还需兼顾市场竞争环境、顾客出价能力、营销发行体系等多方因素。
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[1]独立同分布是中心极限定理和辛钦大数定律成立的必要条件。中心极限定理阐明了即使原来并不服从正态分布的独立同分布的随机变量,它们的总和(或者均值)的分布渐近地服从正态分布;辛钦大数定律表明大量的独立同分布的随机变量依概率收敛于平均值。它们都揭示出大样本具有稳定性的规律,成为保险业务赖于存在的数理基础。
[2]这里有几个术语需要稍作区别。经验费率(experience rating),或称为费率增减法(merit rating),是依据被保险人过去的实际损失经验调整其初始保费的做法,一般以过去若干年的平均赔付为基础来浮动费率,以反映保险标的的差异性。车险中普遍采用的奖惩系统或者无赔款优待系统是经验费率的特例,两者都是依据理赔次数而不是理赔金额来调整初始保费;相比之下,奖惩系统的费率浮动幅度比无赔款优待系统大得多,前者实行奖优罚劣的双向浮动,而后者只实行单向减费浮动,即不发生赔付时享受费率折扣,而发生赔付时维持原有费率不变。在我国,尽管车险费率浮动机制早已实现了从无赔款优待系统到奖惩系统的升级,但是由于“无赔款优待”概念引入我国的时间较长,社会认同度较高,当前的车险条款仍沿用“无赔款优待”概念表述“奖惩系统”。
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[2]这篇论文的第1作者和第2作者分别是中国人民大学的孟生旺教授和袁卫教授。
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[1]目前为止,韩国被认为是世界上唯一采用考虑索赔大小的BMS的国家(崔树贤和邵学清,2006)。
[2][美]让·勒梅尔.汽车保险费的定价原理[M].袁卫译.北京:经济科学出版社,1997.pp 158.
[1]Loimaranta(1972)根据马尔可夫链的性质,指出当奖励系统满足以下条件时:(1)特定保单在单个保险期内的索赔次数的概率分布与具体的保险期无关(即是时齐的),(2)无索赔概率p_0(λ)＞0,概率转移矩阵存在稳定状态,那么马尔可夫链是遍历的。
[1]奖惩系统被认为具有激励投保人谨慎行车的作用,这样索赔次数表现出负传染性(ncgative contagion),即前期报告索赔的投保人今后发生索赔的可能性小于未报告索赔的投保人。当然,还有一种主流观点认为汽车保险的承保风险是外生的(exogenous),所以索赔事故具有正传染性(positive contagion)。
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[1]与超额收费相对应的是不足收费(undercharge),但超额收费更受关注。从管理者的角度看,对超额收费和不足收费不应该一视同仁,向投保人超额收费比不足收费要严重得多(Lemaire,1995)。实际上,财务稳定的奖惩系统在对高风险投保人超额收费的同时,必然在对低风险投保人不足收费。因此,消除超额收费或不足收费是实现BMS“费用再分配的合理性”这一相同目标的不同路径。
[2][美]让·勒梅尔.汽车保险费的定价原理[M].袁卫译.北京:经济科学出版社,1997.pp 152-157.
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[2]Baionne,E,S.Levantesi & M.Menzietti.The development of an optimal Bonus-Malus System in a competitive market[J].ASTIN Bulletin,2002,32(1):159-170.pp 162.
[1]该篇论文的第1作者和第2作者分别是中国人民大学的肖宇谷博士和孟生旺教授。
[2][美]让·勒梅尔.汽车保险费的定价原理[M].袁卫译.北京:经济科学出版社,1997.pp 6.
[1]关于“合约时间效应”的具体说明参见本文第25页。
[2]克里斯汀·蒙特和丹尼尔·塞拉(2005)对“博弈”和“决策”作了区别。博弈论(又称对策论)足分析多个参与者之间相互影响时策略的均衡问题,而决策论是讨论单一参与者最优策略的选择问题。决策论也可以视为一种特殊的双人博弈,只不过其中一方是一个虚拟的参与者——“自然”,另一方的效用由他(她)的决策和自然状态共同决定。因此,两者的区别:决策问题中的不确定性只来源于“自然”的随机步,博弈问题中的不确定性是由于对手策略的预期是外生的。
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[1]从狭义上讲,保险欺诈专指投保人利用不正当手段谋取保险金的行为,具体表现为虚构保险标的、编造保险事故、跨大损失程度等。从广义上来看,保险欺诈的发起人不仅包括投保人,还可能包括保险人、保险中介人,如保险人以不合理的保险条款和费率承保业务,保险代理人误导投保人、私吞保费、造假赔案等(边文霞,2006)。归结起来,保险欺诈是泛指欺诈者利用保险谋求不当利益的行为。考虑到BMS的受用者仅为投保人,本文研究采纳狭义的保险欺诈概念。
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[1]首次索赔决定了保费调整的方向(奖励或惩罚),较之后续索赔对于投保人的影响更大,因此首次索赔时点更能反映投保人在BMS条件下的行为偏好。
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