基于Gamma随机效应分层贝叶斯模型的汽车延保定价

Hierarchical Bayesian Models with Gamma Random Effect in Rating for Vehicle Extended Warranty Contract

汽车延保在中国方兴未艾,相应保险产品的推出更是必然趋势,但相关精算定价研究仍为空白。假设系统故障过程为更新过程,将故障分析问题转换为生存分析问题,对存在左截断和右删失的选择性样本进行分析;模型构建上,假设汽车系统寿命服从两参数威布尔分布,构造多层贝叶斯模型,基于MCMC方法估计后验参数;在第二层模型中引入地区、车型、系统等因子作为协变量建立威布尔混合效应模型,并假设随机效应服从Gamma分布,考虑到系统内部件存在竞争风险,对系统寿命分布参数进行调整,把系统寿命的建模分析转换为指定时间内故障次数的分析,并据此给出延保产品精算定价;通过实证研究,基于某4S店真实数据给出两年期延保定价,结果表明基于Gibbs抽样的贝叶斯MCMC方法估计结果收敛性较好,最终定价也贴合实际情况。

Vehicle extended warranty is an emerging market in China and the promotion of corresponding insurance is an inevitable trend.However,academic-related research is almost blank about rating for it.Given the selective samples with left truncated and right censored data,we translate fault analysisinto survival analysis by assuming that system fault process is a renewal process.The posterior parameters of system survival time which is assumed to follow Weibull distribution are estimated through a hierarchical Bayesian model based on MCMC methods.In second hierarchy,a mixed-effects model is introduced with fixed effects including region,model and system and Gamma random effects.Furthermore,the estimated parameters need to be adjusted because there are competing risks among parts in one system.Then the system life can be translated into times of faults within the time specified.An empirical study is done to price a two-year auto extended warranty based on real data from some authorized dealer.And the results of Bayesian MCMC methods based on Gibbs sampling indicate that this method is of better convergence.