TY - JOUR
T1 - Calibration of transition intensities for a multistate model
T2 - Application to long-term care
AU - Esquível, Manuel L.
AU - Guerreiro, Gracinda R.
AU - Oliveira, Matilde C.
AU - Real, Pedro Corte
N1 - UID/MAT/00297/2020
PY - 2021/2/8
Y1 - 2021/2/8
N2 - We consider a non-homogeneous continuous time Markov chain model for Long-Term Care with five states: the autonomous state, three dependent states of light, moderate and severe dependence levels and the death state. For a general approach, we allow for non null intensities for all the returns from higher dependence levels to all lesser dependencies in the multi-state model. Using data from the 2015 Portuguese National Network of Continuous Care database, as the main research contribution of this paper, we propose a method to calibrate transition intensities with the one step transition probabilities estimated from data. This allows us to use non-homogeneous continuous time Markov chains for modeling Long-Term Care. We solve numerically the Kolmogorov forward differential equations in order to obtain continuous time transition probabilities. We assess the quality of the calibration using the Portuguese life expectancies. Based on reasonable monthly costs for each dependence state we compute, by Monte Carlo simulation, trajectories of the Markov chain process and derive relevant information for model validation and premium calculation.
AB - We consider a non-homogeneous continuous time Markov chain model for Long-Term Care with five states: the autonomous state, three dependent states of light, moderate and severe dependence levels and the death state. For a general approach, we allow for non null intensities for all the returns from higher dependence levels to all lesser dependencies in the multi-state model. Using data from the 2015 Portuguese National Network of Continuous Care database, as the main research contribution of this paper, we propose a method to calibrate transition intensities with the one step transition probabilities estimated from data. This allows us to use non-homogeneous continuous time Markov chains for modeling Long-Term Care. We solve numerically the Kolmogorov forward differential equations in order to obtain continuous time transition probabilities. We assess the quality of the calibration using the Portuguese life expectancies. Based on reasonable monthly costs for each dependence state we compute, by Monte Carlo simulation, trajectories of the Markov chain process and derive relevant information for model validation and premium calculation.
KW - Life expectancy
KW - Long-term care insurance
KW - Monte carlo simulation
KW - Multi-state models
KW - Transition intensities
UR - http://www.scopus.com/inward/record.url?scp=85101168717&partnerID=8YFLogxK
U2 - 10.3390/risks9020037
DO - 10.3390/risks9020037
M3 - Article
AN - SCOPUS:85101168717
SN - 2227-9091
VL - 9
SP - 1
EP - 17
JO - Risks
JF - Risks
IS - 2
M1 - 37
ER -