零膨胀贝叶斯非参数模型对车险索赔频率的估计
Estimation of Auto Insurance Claim Frequency by a Zero-Expansion Bayesian Nonparametric Model

在非寿险精算领域，往往数据中会出现大量的零次索赔情况，这一零聚集现象称为零膨胀现象。在保险实务中，导致零膨胀现象的原因有多方面：比如某些保险产品在设计时就设定了较高的理赔门槛，导致很多小额理赔无法触发，从而产生大量的零值数据；或是在保险期限内被保险人没有出险因而没有产生索赔等。为了拟合数据中过多的零值，用零膨胀模型是一种很有效的方法。目前精算中领域中解决零膨胀问题大多使用的零膨胀模型，都用传统的参数估计方法进行参数估计，都局限在有限维的参数空间中。本研究使用贝叶斯非参数模型，它是一种定义在无限维参数空间上的贝叶斯模型，其大小可以随着模型内数据的增大或减小而自适应模型的变化。因此，将贝叶斯非参数方法引入零膨胀问题中，使得模型综合了贝叶斯方法和非参数方法的诸多优点，具有更大的灵活性。对解决保险精算领域中的问题具有重要的理论意义与实际应用价值。
In the field of non-life actuarial science, there are often a large number of zero claims in the data, and this zero aggregation phenomenon is called zero inflation. In insurance practice, there are many reasons for the phenomenon of zero inflation: for example, some insurance products are designed with a high claim threshold, resulting in many small claims that cannot be triggered, resulting in a large amount of zero-value data, or the insured does not have an insurance during the insurance period and therefore does not generate a claim. In order to fit too many zeros in the data, a zero-inflation model is an effective method. At present, most of the zero-dilation models used to solve the zero-dilation problem in the actuarial field use traditional parameter estimation methods for parameter estimation, which are limited to the finite-dimensional parameter space. In this study, we use a Bayesian nonparametric model, which is a Bayesian model defined on an infinite-dimensional parametric space, the size of which can adapt to the change of the model as the data within the model increases or decreases. Therefore, the Bayesian nonparametric method is introduced into the zero-expansion problem, which makes the model combine many advantages of Bayesian method and non-parametric method, and has greater flexibility. It has important theoretical significance and practical application value for solving problems in the field of actuarial science.