The idea of forward rates stems from interest rate theory. It has natural connotations to transition rates in multi-state models. The generalisation from the forward mortality rate in a survival model to multi-state models is non-trivial and several definitions have been proposed. We establish a theoretical framework for the discussion of forward rates. Furthermore, we provide a novel definition with its own logic and merits and compare it with the proposals in the literature. The definition turns the Kolmogorov forward equations inside out by interchanging the transition probabilities with the transition intensities as the object to be calculated.

中文翻译：

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前进过渡率

远期利率的思想源于利率理论。对于多状态模型中的转换速率，它具有自然的含义。从生存模型中的前瞻性死亡率到多状态模型的泛化是不平凡的，已经提出了几种定义。我们建立了讨论远期汇率的理论框架。此外，我们提供了一个具有其自身逻辑和优点的新颖定义，并将其与文献中的建议进行了比较。该定义通过将跃迁概率与跃迁强度作为要计算的对象进行互换，使Kolmogorov正向方程式由内而外。