In this paper, we consider the problem of experience rating within the classic Markov chain life insurance framework. We begin by investigating various multivariate mixed Poisson models with mixing distributions encompassing independent Gamma, hierarchical Gamma, and multivariate phase-type. In particular, we demonstrate how maximum likelihood estimation for these proposed models can be performed using expectation-maximization algorithms, which might be of independent interest. Subsequently, we establish a link between mixed Poisson distributions and the problem of pricing group disability insurance contracts that exhibit heterogeneity. We focus on shrinkage estimation of disability and recovery rates, taking into account sampling effects such as right-censoring. Finally, we showcase the practicality of these shrinkage estimators through a numerical study based on simulated yet realistic insurance data. Our findings highlight that by allowing for dependency between latent group effects, estimates of recovery and disability rates mutually improve, leading to enhanced predictive performance.

翻译：本文在经典马尔可夫链人寿保险框架下探讨经验费率厘定问题。首先，我们研究了多种多元混合泊松模型，其混合分布涵盖独立伽马分布、分层伽马分布及多元相型分布。特别地，我们展示了如何通过期望最大化算法对这些模型进行最大似然估计，该方法本身可能具有独立的研究价值。随后，我们建立了混合泊松分布与存在异质性的团体伤残保险合约定价问题之间的联系。重点探讨了考虑右删失等抽样效应时，伤残率与康复率的收缩估计方法。最后，通过基于模拟但贴近现实的保险数据进行的数值研究，我们验证了这些收缩估计量的实用性。研究结果表明，通过允许潜在群体效应之间存在依赖性，伤残率与康复率的估计能够相互促进，从而提升预测性能。