copula函数信度模型在风险定价中的应用——基于我国车险数据

Application of Copula Credibility Model in Ratemaking——Based on Auto Insurance Data

信度模型能够刻画风险类别组内的相关性,是风险定价中应用最广泛的模型之一。相较传统信度模型,基于copula函数的信度模型能够突破传统信度模型变量间的相关性不随时间变化的假设限制。本文将copula函数信度模型应用到我国车辆损失保险的定价中,以广义线性模型作为边际分布,利用t-copula函数度量赔付变量间的时间相关性,建立多元联合分布,并计算赔付金额的未来分布和预测值。实证结果表明不同地区车辆损失保险的赔付情况有差异,当年赔付金额对后续赔付的影响随时间减弱;t-copula函数AR(1)形式相关系数矩阵的信度模型的预测误差最小,预测结果优于传统信度模型,说明copula函数信度模型在风险定价的实践工作中有应用价值。

The credibility model can characterize the dependencies among claims within a risk class, which is one of the most widely used models in ratemaking. Compared to the traditional credibility models, Copula credibility model can relax the assumption that dependencies among claims are constant over time. In this article, we applied- Copula credibility model to auto own-damage insurance ratemaking, using generalized linear model as the marginal distributions and t-copula measuring correlations among claims. We built a multivariate joint distribution to generate predictive distributions and compute the predictors of claims. The empirical results show that average claims of auto own-damage insurance show regional disparities and the claim experience of current year poses diminishing influence on claims of the following years. The t-copula credibility with AR （ 1 ） correlation matrix displays the minimum sum of squared prediction errors and gets better predictors than traditional credibility models, which means that Copula credibility model is a valuable tool in ratemaking practice.