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

Manuel L. Esquível (), Nadezhda P. Krasii and Gracinda R. Guerreiro
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Manuel L. Esquível: Department of Mathematics, NOVA FCT, and NOVA Math, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Monte de Caparica, Portugal
Nadezhda P. Krasii: Department of Higher Mathematics, Don State Technical University, Gagarin Square 1, Rostov-on-Don 344000, Russia
Gracinda R. Guerreiro: Department of Mathematics, NOVA FCT, and NOVA Math, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Monte de Caparica, Portugal

Mathematics, 2024, vol. 12, issue 5, 1-21

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.

Keywords: Markov chains; non homogeneous; continuous time; regime switching processes; estimation; calibration; health insurance; long-term care (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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