Modélisation semi-markovienne de la perte d'autonomie chez les personnes âgées : application à l'assurance dépendance

Abstract : Alongside the increase in life expectancy observed in developed countries since the beginning of the 20th century , numerous challenges arise for modern societies. Among them the loss of autonomy in elderly people, also known as Long-Term Care (LTC). Long-term care may be defined as a state of incapacity to perform autonomously part of the Activities of Daily Living (ADL). In most cases, long-term care is caused by one or several pathologies linked to aging. Disabled people therefore require help provided by a relative or professional caregiver or may even need to enter a nursing home. In France, a public aid called the Allocation Personnalisée pour l’Autonomie (APA), literally customized aid for autonomy, aims at covering the expenses caused by long-term care. Nevertheless, the amount of benefit is relatively small in regards of those expenses. Therefore, many insurers have designed products dedicated to complement the public aid. In order to price those products and monitor the risk, insurers need to model the long-term care process. In most cases, one rely on multi-state modeling with states autonomy, death and one or several levels of LTC. To predict the risk one has to assess the transition probabilities between states. Under the Markov assumption, those probabilities are considered to only depend on the current state. As regards the study of LTC, this assumption may be seen as too restrictive to account for the complexity of the underlying risk. In a semi-Markov framework, those probabilities may also depend on the time spent in the current state. In this thesis, we emphasis the necessity of the semi-Markov modeling. We demonstrate the impact of time spent in LTC on death probabilities. Besides, we exhibit that taking into account the diversity induced by pathologies leads to sizable improvements in the fit of the model to experience data. Furthermore, we highlight that the peculiar shape taken by death probabilities as a function of time spent in LTC may be explained by the mixture of pathology groups among the disabled population. The first chapter of this thesis provides an introduction of the long-term care risk and different tools to quantify it. The second chapter focuses on death probabilities among disabled, using the APA database. In the third chapter, we introduce a fully parametric approach to estimate transition probabilities in a model with a single state of LTC, relying on data from an insurance portfolio. Lastly, the fourth chapter study transition probabilities for 4 distinct groups of pathologies: cancer, neurological diseases, dementia and other causes. This validates the empirical results obtained in the previous chapters.
Document type :
Complete list of metadatas
Contributor : Guillaume Biessy <>
Submitted on : Wednesday, December 28, 2016 - 6:16:15 PM
Last modification on : Friday, July 20, 2018 - 11:13:29 AM
Long-term archiving on : Tuesday, March 21, 2017 - 5:57:07 AM


  • HAL Id : tel-01423193, version 1



Guillaume Biessy. Modélisation semi-markovienne de la perte d'autonomie chez les personnes âgées : application à l'assurance dépendance. Applications [stat.AP]. Université Paris-Saclay; Université d'Evry Val d'Essonne, 2016. Français. ⟨tel-01423193⟩



Record views


Files downloads