Roxane Turcotte, PhD.

Doctorat en mathématiques
UQAM

2023/08

Direction de recherche:

  • Jean-Philippe Boucher, professeur au Département de mathématiques de l’Université du Québec à Montréal

Thèse de doctorat:

Turcotte, Roxane (2023), « Approches statistiques semi-paramétriques pour la modélisation du risque en assurance automobile », Dir.: Jean-Philippe Boucher, Thèse de doctorat. Montréal (Québec, Canada), Université du Québec à Montréal, Doctorat en mathématiques.

Publications

  • R.Turcotte & J.-P. Boucher (2023), GAMLSS for Longitudinal Multivariate Claim Count Models, North American Actuarial Journal, 1-24.

    By generalising GAMs, GAMLSSs allow parametric or semi-parametric modelling of one or more parameters of distributions which are not members of the linear exponential family. Consequently, these GAMLSS approaches offer an interesting theoretical framework to allow the use of several potentially helpful distributions in actuarial science. GAMLSS theory is coupled with longitudinal approaches for counting data because these approaches are essential to predictive pricing models. Indeed, they are mainly known for modelling the dependence between the number of claims from the contracts of the same insured over time. Considering that the models’ cross-sectional counterparts have been successfully applied in actuarial work and the importance of longitudinal models, we show that the proposed approach allows to quickly implement multivariate longitudinal models with non-parametric terms. This semi-parametric modelling is illustrated using a dataset from a major insurance company in Canada. An analysis is then conducted on the improvement of predictive power that the use of historical data and non-parametric terms in the modelling allows. Our approach differs from previous studies by the fact that it does not use any simplifying assumptions as to the value of the a priori explanatory variables and that we have carried out a predictive pricing integrating non-parametric terms within the framework of the GAMLSS in an explicit way, which makes it possible to reproduce the same type of study using other distributions.

  • R.Turcotte, H.Cossette & M.Pigeon (2021), Working with a Parametric Copula-Based model for Individual Non-Life Loss Reserving, Variance, 14(2).

    In this paper, we propose a generalization of the individual loss reserving model introduced by Pigeon et al. (2013) considering a discrete time framework for claims development. We use a copula to model the potential dependence within the development structure of a claim, which allows a wide variety of marginal distributions. We also add a specific component to consider claims closed without payment. We provide a case study based on a detailed personal auto insurance data set from a North American insurance company.

  • J.-P. Boucher & R.Turcotte (2020), A Longitudinal Analysis of the Impact of Distance Driven on the Probability of Car Accidents, Risks, 8(3), 91.

    Using telematics data, we study the relationship between claim frequency and distance driven through different models by observing smooth functions. We used Generalized Additive Models (GAM) for a Poisson distribution, and Generalized Additive Models for Location, Scale, and Shape (GAMLSS) that we generalize for panel count data. To correctly observe the relationship between distance driven and claim frequency, we show that a Poisson distribution with fixed effects should be used because it removes residual heterogeneity that was incorrectly captured by previous models based on GAM and GAMLSS theory. We show that an approximately linear relationship between distance driven and claim frequency can be derived. We argue that this approach can be used to compute the premium surcharge for additional kilometers the insured wants to drive, or as the basis to construct Pay-as-you-drive (PAYD) insurance for self-service vehicles. All models are illustrated using data from a major Canadian insurance company.

Présentations scientifiques

  • Longitudinal Claim Count Models Using Splines For Predictive Ratemaking, Séminaire d’actuariat de l’Université du Connecticut, Virtuel, 1er novembre 2022.
  • Longitudinal Claim Count Models Using Splines For Predictive Ratemaking, 3rd Waterloo Student Conference in Statistics, University of Waterloo, Canada (ON), 14 octobre 2022.
  • Longitudinal Claim Count Models Using Splines For Predictive Ratemaking, Actuarial Research Conference (ARC), University of Illinois, Urbana-Champaign, USA (IL), 3 août 2022.
  • A Longitudinal Analysis Of The Impact Of Distance Driven On The Probability Of Car Accidents, Congrès annuel de la Société statistique du Canada, Virtuel, 7 juin 2021.
  • Ratemaking With Telematics Data, Casualty Actuaries of Greater New York (CAGNY) Spring Meeting, Virtuel, 16 avril 2021.
  • Longitudinal Analysis Of Distance Traveled Ratemaking, Ratemaking, Product and Modeling Virtual Seminar of the Casualty Actuarial Society, Virtuel, 15 mars 2021.

Implications

Présentations locales

  • Modèles de fréquence longitudinaux et semi-paramétriques pour la tarification prédictive, Séminaire de la Chaire Co-operators en analyse des risques actuariels, UQAM, Montréal, Canada (QC), 1er août 2022.
  • A Longitudinal Analysis Of The Impact Of Distance Driven On The Probability Of Car Accidents, Séminaire d’été d’actuariat et de statistique de l’UQAM, Virtuel, 1er juillet 2021.
  • Analyse longitudinale de l’impact de la distance conduite sur la probabilité d’accidents de voitures, 2e Atelier de la Chaire CARA , UQAM, Montréal, Canada (QC), 29 novembre 2019.

Enseignement

Démonstrations

Autres

  • Co-responsable du programme scientifique du Congrès canadien des étudiants en statistique (2022)
  • Co-organisatrice de la Compétition montréalaise en science des données (2022, 2023)
  • Membre de l’Association étudiante des cycles supérieurs en mathématiques (2020, 2021, 2022, 2023)
  • Co-organisatrice du Séminaire d’été de l’Association étudiante des cycles supérieurs en mathématiques (2022)