基于已决赔款与已报案赔款相关性的随机性准备金进展法

Stochastic Reserve Development Method Based on the Correlation between the Paid Payments and the Incurred Payments

随着我国保险业精算技术的普及与发展,目前对准备金波动性的研究已成为一个新方向,准备金评估随机性方法已在国内保险业得到认可和应用。本文创新性地研究了如何将已决赔款和已报案赔款数据的相关性引入到随机性准备金评估方法中,提出了两种基于相关性的随机性准备金进展法,并通过精算实务中的数值实例,应用R软件加以实证分析。本文的研究对保险公司在准备金评估方法中引入并发展随机性方法,具有十分重要的理论意义和实践价值,也为保险行业开发新的准备金评估软件提供有益的支持和参考。

With the popularity and development of actuarial techniques in China＇s insurance industry, the reserves volatility has become a new research topic. The stochastic reserving methods have been recognized and applied in the domestic insurance industry. The paper proposes to study how to introduce the correlation between the paid payments and the incurred payments into stochastic reserving methods, and suggests two stochastic reserve development methods based on the correlation, in order to take account of the correlation between the paid payments and the incurred payments. The first method is a parametric bootstrap method based on bivariate normal distribution, which corresponds to a special copula, i.e., Gaussian copula. The second method is a non-parametric bootstrap method based on resampling pairwise. Numerical illustrations from actuarial practice are provided with R software as positive analysis. We obtain the simulated predictive distributions for the outstanding claims liabilities, as well as the distribution characteristics such as the mean, variance, and percentiles. It is seen that the results from the two methods are very close. The results of the paper have important theoretical significance and practical value for stochastic reserving methods to be introduced and developed into insurance companies, and provide a useful support and reference in developing new reserving software for the insurance industry.