贝叶斯非线性分层模型在多元索赔准备金评估中的应用

本文将贝叶斯非线性分层模型应用于基于不同业务线的多元索赔准备金评估中，设计了一种合适的模型结构，将非线性分层模型与贝叶斯方法结合起来，应用WinBUGS软件对精算实务中经典流量三角形数据进行建模分析，并使用MCMC方法得到了索赔准备金完整的预测分布。这种方法扩展并超越了已有多元评估方法中最佳估计和预测均方误差估计的研究范畴。在贝叶斯框架下结合后验分布实施推断对非寿险公司偿付能力监管和行业决策具有重要作用。

The Application of Bayesian Non-linear Hierarchical Model in Multivariate Claims Reserving

The paper innovatively proposed a Bayesian non-linear hierarchical model for multivariate stochastic claims reserving based on different business lines, designed a suitable model structure through combining non-linear hierarchical model with Bayesian method, so as to provide some numerical analysis for the classic run off triangles data in the actuarial practice with WinBUGS software, and further obtained the complete predictive distributions of claims reserves under the hierarchical model structure using MCMC stochastic simulation method. The proposed method extends and goes beyond best estimators and estimators of mean square error of prediction for claims reserves at the present multivariate claims reserving methods. The ability of the Bayesian framework to carry out simultaneous inference based on the joint posterior distributions is of great importance for non-life insurance solvency monitoring and industry decision making.