Calibrating intensities for long-term care multiple-state Markov insurance model

Abstract

Multiple-state Markov models for life or health insurance have been studied for a considerable amount of time (Christiansen, in Multiple-state models in health insurance, 2012; Helwich, in Durational effects and non-smooth semi-Markov models in life insurance, 2008; Koller, in Stochastische Modelle in der Lebensversicherung, 2000). Given the ease and straight forward way of modelling complex tariffs within the modelling framework of multiple-state Markov models it is surprising to observe that these models still await wide-spread use. Having introduced tariffs for private, supplementary long-term care insurance in the Austrian private health insurance market, the biggest obstacle for using a multiple-state Markov model has been its calibration of the underlying state-change intensities to empirical data. These difficulties were addressed by developing and applying a method to extract state-change intensities from published empirical observations of prevalence rates under assumptions that were deemed sufficient for a portfolio of contracts providing recurring payments dependent on degree of severity of long-term care need. The method developed is described in detail, the used empirical data and derived results are given. This paper is intended to foster further discussion and research regarding calibration methods for advanced insurance models.