For nearly three centuries, actuaries have relied on commutation numbers to model life insurance risks. These techniques are rooted in tabular approaches based on deterministic assumptions and have proved to be highly effective in an era of limited computational power and relatively simple product designs.
Andrey Markov, born in 1856, is widely regarded in the actuarial community for his scientific contributions. Among his most famous works are the Markov Process and the Markov Chain, which are well established in the insurance industry to solve a multitude of statistical problems.
We recognise that a Markov approach employs well-established recursive valuation techniques. Further, in combination with Thiele’s differential equation, an iterative valuation of state-dependent insurance obligations can be performed. Applications are manifold and range from modern ratemaking and reserving, to forecasting of the insured’s benefits. While we provide some theoretical background on the idea of Markov models, our focus is to look at some real-life examples for modelling life insurance contracts. Finally, our practical observations on designing actuarial kernels for policy administration systems when using Markov approaches in the context of system migrations are summarised.
