Calculation of LTC Premiums based on direct estimates of transition probabilities

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Discussion Paper ; No. 393

Classification and Topics

• Subject: Markovian Multi-State Model ; Transition Probabilities ; Aalen-Johansen Estimator ; Pseudo-Values ; GLM ; GEE ; LTC ; Premium

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Helms, Florian ; Czado, Claudia ; Gschlößl, Susanne
• Event: Veröffentlichung
• (who): Ludwig-Maximilians-Universität München, Sonderforschungsbereich 386 - Statistische Analyse diskreter Strukturen
• (where): München
• (when): 2004

Further information

• DOI: doi:10.5282/ubm/epub.1763
• Handle: http://hdl.handle.net/10419/31064
• URN: urn:nbn:de:bvb:19-epub-1763-2
• Last update: 10.03.2025, 11:43 AM CET