（南开大学经济学院风险管理与保险学系）

【摘  要】在寿险中，多状态模型是传统的两状态模型的推广。多状态模型包括失能、退保等其它状态。在本文中我们将马尔可夫链应用于多状态模型的研究，多元风险模型、多元生命模型都可以视为特殊的多状态模型，从而可以进行统一的处理。传统寿险精算理论中对多元风险模型、多元生命模型和多状态模型分别讨论，本文的统一化处理是很大的改进。本文给出了两个多状态模型的实际应用的例子，对相应的Thiele微分方程组，通过编程求得数值解。

关键词：马尔可夫链 多状态模型 净保费 寿险准备金 Thiele微分方程

中图分类号  F840.62                    文献标识码  A

Applications of Continuous Time Markov Chains in Multiple States Models in Life Contingencies

Abstract: In life insurance, multiple state models are extensions of the traditional two state models. Multiple state models also include many other states such as disabled, withdrawal etc. In this paper we apply Markov chains to the study of multiple state models, both multiple decrement models and multiple life models can be treated as special multiple state models, thus they can be processed in a unified way. The unified processing in this paper is a great improvement to traditional life contingency theory which discusses multiple decrement models, multiple life models and multiple state models separately. Two illustrative practical examples are provided in this paper. The numerical conclusion can be obtained by solving certain Thiele’s differential equations numerically, and the numerical solutions of Thiele’s equations can be obtained using programming.

Key words: Markov chains; multiple state models; net premium; life insurance reserves; Thiele’s differential equations.