Use of Markov Chain Simulation in Long Term Care Insurance

Vladimír Mucha, Ivana Faybíková, Ingrid Krčová

Statistika, 102(4): 409-425
https://doi.org/10.54694/stat.2022.20

Abstract
The aim of this paper is to present the use of simulations of non-homogeneous Markov chains in discrete time in the context of the problem of long-term care delivery. The object of investigation is to model the distribution of clients into different states during specified time steps, then to estimate the average time a client stays in a given state, as well as to estimate the insurance premiums. Within the use of the Monte Carlo simulation method, the focus is on providing approaches that ensure more accurate results in the context of the number of simulations performed. Based on the statistical processing of the data obtained from the simulations, it is possible to obtain the information necessary for the provision of resources for the provision of health care and for the determination of the aforementioned premiums. For the implementation of the above techniques and their graphical presentation available packages such as markovchain, ggplot2 or custom code created using the R language were used.

Long-term care insurance, Markov Chains, multi-state models, simulations, Monte Carlo Method, markovchain package