EconPapers    
Economics at your fingertips  
 

Non-parametric inference of transition probabilities based on Aalen–Johansen integral estimators for acyclic multi-state models: application to LTC insurance

Quentin Guibert and Frédéric Planchet

Insurance: Mathematics and Economics, 2018, vol. 82, issue C, 21-36

Abstract: Studying Long Term Care (LTC) insurance requires modeling the lifetime of individuals in presence of both terminal and non-terminal events which are concurrent. Although a non-homogeneous semi-Markov multi-state model is probably the best candidate for this purpose, most of the current researches assume, maybe abusively, that the Markov assumption is satisfied when fitting the model. In this context, using the Aalen–Johansen estimators for transition probabilities can induce bias, which can be important when the Markov assumption is strongly unstated. Based on some recent studies developing non-Markov estimators in the illness–death model that we can easily extend to a more general acyclic multi-state model, we exhibit three non-parametric estimators of transition probabilities of paying cash-flows, which are of interest when pricing or reserving LTC guarantees in discrete time. As our method directly estimates these quantities instead of transition intensities, it is possible to derive asymptotic results for these probabilities under non-dependent random right-censorship, obtained by re-setting the system with two competing risk blocks. Inclusion of left-truncation is also considered. We conduct simulations to compare the performance of our transition probabilities estimators without the Markov assumption. Finally, we propose a numerical application with LTC insurance data, which is traditionally analyzed with a semi-Markov model.

Keywords: Multi-state model; Aalen–Johansen integral; Non-parametric estimator; Non-Markov process; LTC insurance (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167668716305297
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:82:y:2018:i:c:p:21-36

DOI: 10.1016/j.insmatheco.2018.05.004

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

More articles in Insurance: Mathematics and Economics from Elsevier
Bibliographic data for series maintained by Haili He ().

 
Page updated 2020-05-02
Handle: RePEc:eee:insuma:v:82:y:2018:i:c:p:21-36