Research On Bonus-Malus System In Motor Insurance Under Behavioral Game

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.