This research develops the scheme proposed in the paper Pollard [J Inst Actuar 96(2): 251–264, 1970], which is based on a two-state model for the analysis of 1-year mortality, but the results are also valid for the probabilities related to other types of insurance events such as disablement and accidents. We extend the Pollard’s original scheme into time-discrete models with more states (active-invalid-dead) together with further investigation into multi-year time horizon. Additionally, hypotheses for real-valued individual frailty are assumed in the models. As the baseline probabilistic structure, we have adopted a traditional three-state model in a Markov context. We focus on an insurance portfolio. Our outputs of interest are based on the probability distributions of the annual payouts for term insurance policies providing lump sum benefits both in case of death and in case of permanent disability. The analysis of the probability distributions allows us to assess the risk profile of the insurance portfolio, and thus to suggest appropriate actions in terms of premiums and capital allocation. In this regards, we adopt the percentile principle.

本研究开发了 Pollard [J Inst Actuar 96(2): 251–264, 1970] 论文中提出的方案，该方案基于用于分析 1 年死亡率的二态模型，但结果也有效与其他类型的保险事件（如残疾和事故）相关的概率。我们将 Pollard 的原始方案扩展到具有更多状态（活动-无效-死亡）的时间离散模型，并进一步研究了多年时间范围。此外，模型中还假设了对真实值个体虚弱的假设。作为基线概率结构，我们在马尔可夫上下文中采用了传统的三态模型。我们专注于保险组合。我们感兴趣的输出基于定期保险单的年度赔付概率分布，在死亡和永久性残疾的情况下提供一次性赔付。概率分布的分析使我们能够评估保险组合的风险状况，从而就保费和资本分配提出适当的行动建议。对此，我们采用百分位原则。