基于状态空间不可数的Markov跳过程的Thiele微分方程
Thiele's Differential Equation Based on Markov Jump Processes with Non-countable State Space
摘要：
在现代人寿保险中，有限或至少可数状态空间上的连续时间马尔可夫过程多年来一直是被保险人状态建模的重要工具。基于在伤残保险中的应用，本文提出了一种基于马尔可夫跳过程的保险状态模型。我们使用这个模型来推导出一种新型的Thiele微分方程，例如，它允许基于两个参数的连续时间康复率的伤残保险中的储备金的一致计算。
英文摘要：
In modern life insurance, Markov processes in continuous time on a finite or at least countable state space have been over the years an important tool for the modelling of the states of an insured. Motivated by applications in disability insurance, we propose in this paper a model for insurance states based on Markov jump processes with more general state spaces. We use this model to derive a new type of Thiele's differential equation which e.g. allows for a consistent calculation of reserves in disability insurance based on two-parameter continuous time rehabilitation rates.
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