Papers by Jean-Philippe Boucher
Social Science Research Network, 2020
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arXiv (Cornell University), Sep 26, 2022
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Risks, Mar 24, 2021
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Annals of Actuarial Science
In recent papers, Bonus-Malus Scales (BMS) estimated using data have been considered as an altern... more In recent papers, Bonus-Malus Scales (BMS) estimated using data have been considered as an alternative to longitudinal data and hierarchical data approaches to model the dependence between different contracts for the same insured. Those papers, however, did not discuss in detail how to construct and understand BMS models, and many of the BMS’s basic properties were not discussed. The first objective of this paper is to correct this situation by explaining the logic behind BMS models and by describing those properties. More particularly, we will explain how BMS models are linked with simple count regression models that have covariates associated with the past claims experience. This study could help actuaries to understand how and why they should use BMS models for experience rating. The second objective of this paper is to create artificial past claims history for each insured. This is done by combining recent panel data theory with BMS models. We show that this addition significant...
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North American Actuarial Journal, 2020
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ASTIN Bulletin, 2021
ABSTRACTUsing telematics technology, insurers are able to capture a wide range of data to better ... more ABSTRACTUsing telematics technology, insurers are able to capture a wide range of data to better decode driver behavior, such as distance traveled and how drivers brake, accelerate, or make turns. Such additional information also helps insurers improve risk assessments for usage-based insurance, a recent industry innovation. In this article, we explore the integration of telematics information into a classification model to determine driver heterogeneity. For motor insurance during a policy year, we typically observe a large proportion of drivers with zero accidents, a lower proportion with exactly one accident, and a far lower proportion with two or more accidents. We here introduce a cost-sensitive multi-class adaptive boosting (AdaBoost) algorithm we call SAMME.C2 to handle such class imbalances. We calibrate the algorithm using empirical data collected from a telematics program in Canada and demonstrate an improved assessment of driving behavior using telematics compared with tr...
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Journal of Risk and Insurance, 2016
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Caries Research, 2016
Methods for analysing dental caries and associated risk indicators have evolved considerably in r... more Methods for analysing dental caries and associated risk indicators have evolved considerably in recent decades. The use of zero-inflated or hurdle models is increasing so as to take account of the decayed, missing, and filled teeth (DMFT) distribution, which is positively skewed and has a high proportion of zero scores. However, there is a need to develop new statistical models that involve pragmatic biological considerations on dental caries in epidemiological surveys. In this paper, we show that the zero-inflated and the hurdle models can both be expressed as a compound sum. Using the same compound sum, we then present the generalized negative binomial (GNB) distribution for dental caries count data, and provide a numerical application using the data of the EPIPAP study. The GNB model generates the best score functions while handling the lifetime dental caries disease process better. In conclusion, the GNB model suits the nature of some count data, in particular when structural ze...
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La premiere partie de la these s'interesse aux modeles de classification du nombre de reclama... more La premiere partie de la these s'interesse aux modeles de classification du nombre de reclamations sous l'hypothese que toutes les observations analysees dans la base de donnees sont independantes. En introduisant les caracteristique du risque dans la moyenne par une fonction de score, le developpe-ment de ce type de modeles permet de mieux comprendre l'impact de certaines caracteristiques sur la probabilite de reclamer a l'assureur. De plus, en utilisant des modeles qui different de la loi de Poisson, ces travaux permettent une autre interpretation du mecanisme de reclamation a l'assureur. L'effet du bonus-malus, des deductibles ou du changement de perception du conducteur apres un accident sont toutes des explications possibles a la divergence entre le nombre de reclamation et la loi de Poisson. Dans la majorite des situations en assurance, les caracteristiques du risque ne sont pas toutes utilisees dans la tarification, soit parce qu'elles ne sont pas mesurables, soit parce qu'il serait socialement inacceptable de les utiliser. Ainsi, un facteur d'heterogeneite permettant de capturer ces caracteristiques inobservables est ajoute au parametre de moyenne de la loi de Poisson. Ce facteur additionnel, appele heterogeneite, est modelise de facon parametrique ou encore de maniere non-parametrique. Plusieurs methodes peuvent etre envisagees pour determiner la forme non-parametrique de cette heterogeneite. Nous avons analyse ces diverses methodes d'evaluations et compare les resultats avec des methodes completement parametriques. Puisque de nombreux modeles pour donnees de comptage sont utilises, des methodes de comparaisons de modeles ont ete developpees. Certaines sont basees sur les distributions d'estimation des parametres alors que certaines autres se basent sur la distribution du maximum de vraisemblance ou les criteres d'information. Suite a ces analyses et ces comparaisons, nous pouvons voir que la distribution de l'heterogeneite de la loi de Poisson ne peut pas etre directement ajustee avec une distribution parametrique simple. De la meme maniere, nous avons remarque qu'une distribution plus complexe que la loi de Poisson, telles que la distribution a barriere, la binomiale negative X ou les modeles gonfles a zero generent non-seulement un meilleur ajustement que les distributions de Poisson avec heterogeneite, mais que leur utilisation se justifie intuitivement pour les donnees d'assurance. Une grande partie de cette these se consacre justement a l'analyse de ces nouvelles distributions en assurance. De maniere similaire aux travaux effectues selon l'hypothese que tous les contrats d'assurance sont independants, cette section de la these se consacre a l'analyse de modeles avec donnees de panel, supposant donc une dependance entre les contrats d'un meme assure. Intuitivement, cette dependance se justifie en considerant l'effet des variables de classification inconnues qui touchent tous les contrats d'un meme assure, ou encore en considerant l'impact d'un accident sur les habitudes de conduite d'un assure. Ainsi, en se basant sur les lois de Poisson et binomiale negative, divers modeles creant une dependance temporelle entre les contrats d'un meme assure sont etudies. De ces distributions sont aussi calcul��es les primes predictives, c'est-a-dire les primes conditionnelles a un historique de sinistres. Tout comme la partie precedente de la these, diverses interpretations des modeles sont proposees. De maniere assez claire, un seul modele sort du lot: le modele ou un effet aleatoire individuel affecte toutes les observations d'un meme assure. Neanmoins, avant d'utiliser ce modele, une hypothese essentielle d'independance entre les caracteristiques du risque et ce facteur aleatoire doit etre verifiee.[...]
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New models for panel data that consist of a generalization of the hurdle model are presented and ... more New models for panel data that consist of a generalization of the hurdle model are presented and are applied to modeling a panel of claim counts. Correlated random effects are assumed for the two processes involved to allow for dependence among all the contracts held by the same insured. A method to obtain a posteriori distribution of the random effects as well as predictive distributions of the number of claims is presented. A numerical illustration of reported insurance claims shows that if independence between random effects is assumed, then the variance of a priori premiums may be underestimated. If dependence between random effects is considered, then the predicted number of claims given past observations and covariate information and its variance is also larger than the one obtained when independence is assumed.
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SSRN Electronic Journal, 2020
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North American Actuarial Journal, 2022
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Risks, 2021
This article describes the techniques employed in the production of a synthetic dataset of driver... more This article describes the techniques employed in the production of a synthetic dataset of driver telematics emulated from a similar real insurance dataset. The synthetic dataset generated has 100,000 policies that included observations regarding driver’s claims experience, together with associated classical risk variables and telematics-related variables. This work is aimed to produce a resource that can be used to advance models to assess risks for usage-based insurance. It follows a three-stage process while using machine learning algorithms. In the first stage, a synthetic portfolio of the space of feature variables is generated applying an extended SMOTE algorithm. The second stage is simulating values for the number of claims as multiple binary classifications applying feedforward neural networks. The third stage is simulating values for aggregated amount of claims as regression using feedforward neural networks, with number of claims included in the set of feature variables. ...
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arXiv: Applications, 2018
We develop a claim score based on the Bonus-Malus approach proposed by [7]. We compare the fit an... more We develop a claim score based on the Bonus-Malus approach proposed by [7]. We compare the fit and predictive ability of this new model with various models for of panel count data. In particular, we study in more details a new dynamic model based on the Harvey-Fernand\`es (HF) approach, which gives different weight to the claims according to their date of occurrence. We show that the HF model has serious shortcomings that limit its use in practice. In contrast, the Bonus-Malus model does not have these defects. Instead, it has several interesting properties: interpretability, computational advantages and ease of use in practice. We believe that the flexibility of this new model means that it could be used in many other actuarial contexts. Based on a real database, we show that the proposed model generates the best fit and one of the best predictive capabilities among the other models tested.
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This paper proposes a statistical model for claims related to climatic events that exhibit huge v... more This paper proposes a statistical model for claims related to climatic events that exhibit huge volatility both in frequency and intensity, such these caused by tornadoes hitting the US. To duplicate this volatility and the seasonality, we introduce a new claim arrival process modeled by a Poisson process of intensity equal to the product of a periodic function with a multifractal process. The amplitudes of claims are modeled in a similar way, with gamma random variables. We show that this method allows simulation of the peaks of damage. The two dimension multifractal model is also investigated. The work concludes with an analysis of the impact of the model on spreads of weather bonds related to claims caused by tornadoes.
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Papers by Jean-Philippe Boucher