We consider a non-homogeneous continuous time Markov chain model for Long-Term Care with five states, the healthy state, three dependent states of low, intermediate and high dependence and one exit state. The three dependence states choice is based on a short Bartel classification scheme and a clustering analysis recently performed on the more than 120 000 records of Continuing Care National Database for 2015. From this clustering analysis we could extract one year probability transition matrices for five different classes of age. In the multiple state model we allow for non null intensities for all the returns from higher dependence states to all lesser dependence state. We propose a method to calibrate the intensities with the probability transition matrices obtained by the clustering analysis, we solve the Kolmogorov forward equations for the probabilities and assess the quality of the calibration. Based on reasonable monthly costs for each of the dependence states we compute, by Monte Carlo simulation, 1000 trajectories of the Markov chain process and derive relevant information for model validation and for monthly premiums determination.
|Title of host publication||2nd International Conference on Computacional Finance (ICCF 2017), Proceedings|
|Publisher||Universidade de Lisboa|
|Number of pages||6|
|Publication status||Published - 2017|
|Event||2nd International Conference on Computational Finance (ICCF 2017) - Lisbon, Portugal|
Duration: 4 Sep 2017 → 8 Sep 2017
|Conference||2nd International Conference on Computational Finance (ICCF 2017)|
|Period||4/09/17 → 8/09/17|
Esquível, M. L., Oliveira, M. S. P. C. D., Guerreiro, G. R. D., & Nobre, C. I. F. (2017). Calibration and Simulation of a Continuous Time Markov Chain Model for Long Term Care. In 2nd International Conference on Computacional Finance (ICCF 2017), Proceedings (pp. 136-141). Universidade de Lisboa.