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Calculation of LTC Premiums Based on Direct Estimates of Transition Probabilities

Published online by Cambridge University Press:  17 April 2015

Florian Helms ,
Claudia Czado  and
Susanne Gschlößl
Florian Helms
Affiliation:
Technische Universität München, Zentrum Mathematik, Email: florian.helms@web.de
Claudia Czado
Affiliation:
Technische Universität München, Zentrum Mathematik, Email: cczado@ma.tum.de
Susanne Gschlößl
Affiliation:
Technische Universität München, Zentrum Mathematik, Email: susanne@ma.tum.de
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Abstract

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In this paper we model the life-history of LTC-patients using a Markovian multi-state model in order to calculate premiums for a given LTC-plan. Instead of estimating the transition intensities in this model we use the approach suggested by Andersen et al. (2003) for a direct estimation of the transition probabilities. Based on the Aalen-Johansen estimator, an almost unbiased estimator for the transition matrix of a Markovian multi-state model, we calculate so-called pseudo-values, known from Jackknife methods. Further, we assume that the relationship between these pseudo-values and the covariates of our data are given by a GLM with the logit as link-function. Since the GLMs do not allow for correlation between successive observations we use instead the “Generalized Estimating Equations” (GEEs) to estimate the parameters of our regression model. The approach is illustrated using a representative sample from a German LTC portfolio.

Keywords

Markovian Multi-State ModelTransition ProbabilitiesAalen-Johansen EstimatorPseudo-ValuesGLMGEELTCPremium
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 35 , Issue 2 , November 2005 , pp. 455 - 469
Copyright
Copyright © ASTIN Bulletin 2005

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