Estimation–Calibration of Continuous-Time Non-Homogeneous Markov Chains with Finite State Space

Author:

Esquível Manuel L.1ORCID,Krasii Nadezhda P.2ORCID,Guerreiro Gracinda R.1ORCID

Affiliation:

1. Department of Mathematics, NOVA FCT, and NOVA Math, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Monte de Caparica, Portugal

2. Department of Higher Mathematics, Don State Technical University, Gagarin Square 1, Rostov-on-Don 344000, Russia

Abstract

We propose a method for fitting transition intensities to a sufficiently large set of trajectories of a continuous-time non-homogeneous Markov chain with a finite state space. Starting with simulated data computed with Gompertz–Makeham transition intensities, we apply the proposed method to fit piecewise linear intensities and then compare the transition probabilities corresponding to both the Gompertz–Makeham transition intensities and the fitted piecewise linear intensities; the main comparison result is that the order of magnitude of the average fitting error per unit time—chosen as a year—is always less than 1%, thus validating the methodology proposed.

Funder

Fundação para a Ciência e Tecnologia

Publisher

MDPI AG

Reference38 articles.

1. Esquível, M., Guerreiro, G., Oliveira, M., and Real, P. (2021). Calibration of Transition Intensities for a Multistate Model: Application to Long-Term Care. Risks, 9.

2. Vassiliou, P.C.G. (2023). Non-Homogeneous Markov Chains and Systems—Theory and Applications, CRC Press.

3. Pitacco, E. (2014). Health Insurance, Springer.

4. Haberman, S., and Pitacco, E. (1999). Actuarial Models for Disability Insurance, Chapman & Hall/CRC.

5. Billingsley, P. (1961). Statistical inference for Markov Processes, University of Chicago Press. Volume II, Statistical Research Monographs.

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