An Application Of GAM Model To Car Insurance Pricing Under Constraints

Status of car insurance is very important in the property insurance,car insurance pricing models is of great significance for the insurance company’s market share and the assess-ment of the company’s own risk.The car insurance pricing is affected by many factors,and it is a complex,uncertain and nonlinear characteristics of car insurance pricing model.The traditional commonly used the generalized linear model (GLM),although the solution of the random effects of car insurance pricing,without taking into account the presence of continu-ous variables in the nonlinear form,the fitting accuracy of generalized linear models will be greatly reduced. At the same time,in real life, the regulation of insurance market competition or the national policy,the car insurance premiums will be some risk categories limited to a certain range, usually approach is the category of risk premium the critical value,then this part of the cost of transfer to other risk categories,in order to policyholders constitute unfair, will cause the adverse selection of the insured, seriously affect the company’s business.In view of this situation, this paper firstly, generalized additive models (GAM) of the smooth function parameter estimation:Among them, some of the explanatory variables xj are the parameters form, β is the corresponding coefficient,ti is non parametric part of the explanatory variables,fj (·) is a non-parametric function.In order to facilitate the, order p=1,can be obtained from lemma 3.1.1(P13): Among them:Then the structure under the constraint conditions for maximum problem, the model lp(β) is as follows:The formula is a problem with constraint for β, by means of Lagrange extremum, the unconstrained optimization problem into the penalty function: Among them, ζ is a big number, Σ is known.Newton iteration method is used for analysis can be obtained:Finally, the empirical part. By using the iterative method and the language,in the non restraint condition of auto insurance claims data regression parameter estima-tion,at the same time iteration of the auto insurance claims data under the constraint condition, the final results of the analysis and the summary.