Phase-type分布下的信度模型

Credibility Models Based on Phase-Type Distribution

经典信度模型通常假设风险参数的先验分布及索赔的条件分布,并在均方损失函数下推导信度保费。经典信度模型也没有考虑索赔数据会受到通货膨胀因子的影响,这不符合保险公司的期望。基于具有多样性结构的PH分布,在平衡损失函数这个非对称损失函数下,分别讨论了带通货膨胀因子的单合同信度保费和精确信度,并将结果推广到多合同情况。结果表明:在PH分布下能得到更精确有效的保费估计,并使预测结果更加精确。其次,在索赔数据分布未知情况下,得出了如何计算信度保费更符合实际要求的结论。

Classical credibility models usually assume the prior distribution of risk parameters and the conditional distribution of claim data,and derive the credibility premiums under the mean square loss function.The classical credibility models also don’t consider that the claim data will be affected by inflation factors,which doesn’t meet the expectations of insurance companies.Based on the phase-type distribution,this article discussed the single-contract credibility premium and accurate credibility premium with inflation factors under the asymmetrical loss function,and extended the results to the multi-contract.The results showed that a more effective premium estimation be obtained under the PH distribution,and forecast results are more accurate.Secondly,when the distribution of claim data are unknown,this article showed that how to calculate the credibility premiums are more in line with actual requirements.