Pricing for Auto Extended Warranty based on Improved Capture and Recapture Method

The development of auto extended warranty is rising in China, studies on its pricing in the process of exploring, of which a mature system has not been formed. The phenomenon of "high-payment but low-guarantee" is prohibitive for consumers to purchase this kind of service, based on which pricing models of auto extended warranty urgently needs further improvement. 

This article uses the improved frequent capture and recapture method to model claim count. This not only expands the application of the capture and recapture method, but it also has the following two advantages when it is applied to the insurance loss estimation problem: firstly,the model is applicable for incomplete data, not only for data lack of uninsured insurance policies, but also for incomplete data for insured insurance policies.Based on special data such as auto repair data,the hospital data and incomplete company claims records, this model provide a feasible method to estimate insurance losses. The second is that this model takes the dependencies between insurance accidents into account and can naturally deal with the problem of dependencies.

Aiming at the amount of loss, this article aims to compare multiple models,mainly the combination model and mixed model.This paper expands the two common combination distributions into three,and derived the parameter estimation expressions for a total of six distributions of Weibull-Pareto combination and Lognormal-Pareto combination model.In the mixed distribution model, due to the large number of parameters and the existence of invisible variables, it is impossible to obtain the parameter results by directly using the maximum likelihood estimation. This paper uses the EM algorithm to estimate the parameters of the mixed model, and the parameter expressions of multiple K-dimensional homogeneous mixed distributions and multiple 2-dimensional different types of mixed distributions are derived.and summarized the EM algorithm expectation and variance iteration representation of finite-dimensional mixed model.

The empirical analysis part this article uses Copula function to study the relationship between the vehicle age and mileage for auto extended warranty pricing,, then get a specific Copula function to obtain a quantitative two-dimensional joint distribution of vehicle age and mileage, meanwhile the usage rate will be calculated. Secondly, use the usage rate as a price-adjustment factor of auto extended warranty.