Prediction modelling of claim frequency is an important task for pricing and risk management in non-life insurance and needed to be updated frequently with the changes in the insured population, regulatory legislation and technology. Existing methods are either done in an ad hoc fashion, such as parametric model calibration, or less so for the purpose of prediction. In this paper, we develop a Dynamic Poisson state space (DPSS) model which can continuously update the parameters whenever new claim information becomes available. DPSS model allows for both time-varying and time-invariant coefficients. To account for smoothness trends of time-varying coefficients over time, smoothing splines are used to model time-varying coefficients. The smoothing parameters are objectively chosen by maximum likelihood. The model is updated using batch data accumulated at pre-specified time intervals, which allows for a better approximation of the underlying Poisson density function. The proposed method can be also extended to the distributional assumption of zero-inflated Poisson and negative binomial. In the simulation, we show that the new model has significantly higher prediction accuracy compared to existing methods. We apply this methodology to a real-world automobile insurance claim data set in China over a period of six years and demonstrate its superiority by comparing it with the results of competing models from the literature.
翻译:索赔频率的预测建模是非人寿保险中定价和风险管理的一项重要任务,需要随着投保人、监管法规和技术的变化经常更新。现有方法或者以临时方式进行,例如参数模型校准,或者为预测目的采用较少的方法。在本文中,我们开发了动态Poisson国家空间模型,可以在获得新的索赔信息时不断更新参数。DPSS模型既允许时间变化系数,也允许时间变化系数和时间变化系数。考虑到时间变化系数的平稳趋势,在模拟时使用顺畅的样条来模拟时间变化系数。平稳的样条是用最可能的方式客观选择的参数。光滑的参数是用在预定时间间隔前积累的批量数据加以更新,这样就可以更好地接近Poisson公司的基本密度功能。拟议的方法还可以扩大到零膨胀Poisson和负浮度系数的分布假设。在模拟中,我们表明,新模型比现有方法的预测准确性要高得多。我们采用这一方法,用在最可能的可能性来客观地选择了光度参数。我们用这一方法,用在中国的6年中比较了一种真实的优越性索赔数据。我们用在6年的模型中比较了它。我们用了它所比较了一种比较了一种在现实的汽车保险数据。