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Abstract:
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In this paper, we introduce a so-called aggregated Markov chain model in life insurance, where we assign a number of micro states to each biometric macro state, leading to sojourn times in macro states following inhomogeneous phase-type distributions of general dimension. Since the observable data is the trajectories of the macro states only, this extension leads to incomplete data. By assuming piecewise constant transition rates on micro level, we develop algorithms for both parametric and non-parametric estimation of said transition rates using EM algorithms and Markov chain Monte Carlo methods (MCMC), respectively. The talk ends with an application of the algorithms on simulated data from a time-inhomogeneous semi-Markov model, which serves to illustrate possibilities and limitations of our extended model in practical applications.
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