Modelling Multi-State Processes using a Markov Assumption

Many areas of actuarial work involve situations which are conveniently viewed in terms of multi-state processes. Often an individual's presence in a particular state, or movement from one state to another, has some financial impact. The task of the actuary is then to quantify this impact, allowing for the stochastic nature of the process. The use of a Markov assumption in modelling these processes has the advantages of parsimony, mathematical tractability and ease of parameter estimation. In this paper, we show how probabilities and actuarial values may be calculated using a time-homogeneous Markov model. Piecewise constant transition intensities are suggested as a way to extend the approach to the inhomogeneous case. In the event that the Markov assumption is found to be inappropriate, the state space can be modified as an alternative to assuming a more general stochastic process.