Almost all life and health insurance models in the actuarial literature use either a Markov assumption or a semi-Markov assumption. This paper shows that non-Markov modelling is also feasible and presents suitable numerical and statistical tools for the calculation of prospective and retrospective reserves. A central idea is to base the calculation of reserves on forward and backward transition rates. Feasible estimators for the forward transition rates have been recently suggested in the medical statistics literature. This paper slightly extends them according to insurance needs and newly introduces symmetric estimators for backward transition rates. Only few adjustments are actually needed in the classical insurance formulas when switching from Markov modelling to as-if-Markov evaluations in order to avoid model risk.

精算文献中几乎所有的人寿和健康保险模型都使用马尔可夫假设或半马尔可夫假设。本文表明，非马尔可夫模型也是可行的，并为计算预期和追溯储量提供了合适的数值和统计工具。一个中心思想是将储备金的计算基于向前和向后的过渡率。最近在医学统计文献中提出了关于正向跃迁速率的可行估计量。本文根据保险需求对它们进行了略微扩展，并新引入了向后转换率的对称估计。为了避免模型风险，从马尔可夫模型转换为假设马尔可夫模型评估时，古典保险公式中实际上只需要进行很少的调整。