A common approach for pricing insurance contracts consists to represent the insured’s health status by a Markov chain. This article extends this framework by observing this chain on a random scale of time, defined as the inverse of an $\alpha$-stable process. This stochastic clock induces sub-exponential waiting times spent in each state. We first review and extend the properties of this time-change to a conditional filtration at time $t>0$. Next we evaluate a general type of insurance contract from inception to expiry.

中文翻译：

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分数多州保险模型

保险合同定价的一种常见方法是用马尔可夫链表示被保险人的健康状况。本文通过在随机的时间尺度上观察此链来扩展此框架，定义为$\alpha$稳定的过程。此随机时钟会导致在每个状态下花费的指数次等待时间。我们首先回顾一下这种时变的性质，并将其扩展到当时的条件过滤$Ť>0$。接下来，我们评估从开始到到期的一般保险合同类型。