Sébastien Jessup, MSc.

Maitrise en mathématiques
UQAM

2020/04

Direction de recherche:

  • Mathieu Pigeon, professeur au Département de mathématiques de l’Université du Québec à Montréal

Mémoire de maitrise:

Jessup, Sébastien (2020), « Modélisation du risque liée aux primes non-acquises avec dépendance », Dir.: Mathieu Pigeon, Mémoire. Montréal (Québec, Canada), Université du Québec à Montréal, Maîtrise en mathématiques.

La prime non-acquise, ou plus particulièrement le risque associé, n’a que récemment reçu de l’attention des régulateurs. Les pertes non-acquises se produisent après la date d’évaluation pour des contrats souscrits avant cette dernière. Étant donné qu’un modèle d’acquisition inadéquat et une modélisation approximative du passif des primes peut mener à une réserve inexacte pour le risque de la prime non-acquise, un modèle individuel non-homogène des pertes incluant la dépendance entre les couvertures est proposé pour établir une façon alternative d’évaluer ce risque. La survenance des pertes est analysée en termes de la saisonalité et de la fréquence d’implication de couvertures multiples. Des distributions homogènes et non-homogènes sont ajustées aux distributions marginales. Des copules sont ajustées par paire de couvertures en utilisant des méthodes basées sur le rang ainsi qu’une fonction de queue (tail function). Cette approche est appliquée à une base de données automobile récente d’Ontario.

Publications

  • S.Jessup, M.Mailhot & M.Pigeon (2026), Flexible Extreme Thresholds Through Generalised Bayesian Model Averaging, European Actuarial Journal, publication prochaine

    Insurance products frequently provide coverage for potentially significant claims arising from various sources. To model losses from these products appropriately, actuarial models must account for these substantial claims. One effective approach is to use a mixture model that fits a distribution to losses below a certain threshold, while modelling excess losses using extreme value theory. Selecting an optimal threshold, however, remains an open problem without a universally accepted solution. Bayesian Model Averaging (BMA) offers a promising solution by allowing the simultaneous consideration of multiple thresholds. In this paper, we demonstrate that BMA can effectively identify an optimal threshold by combining mixture models, fitting the full distribution accurately, and reduce sensitivity to the choice of threshold. This is shown through simulation studies. We then compare our results with those obtained using automatic threshold selection algorithms, which employ different goodness-of-fit tests, on the well-known Danish reinsurance dataset. Additionally, we apply a similar methodology to identify flexible thresholds based on predictive variables using an automobile claims dataset from a Canadian insurer.

  • S.Jessup, M.Mailhot & M.Pigeon (2025), Uncertainty in Heteroscedastic Bayesian Model Averaging, Insurance: Mathematics and Economics, 121: 63-78

    The literature concerning liability evaluation is very well developed. It is however almost exclusively devoted to the performance of singular models. Recently, a variant of Bayesian Model Averaging (BMA) has been used for the first time to combine outstanding claims models. BMA is a widely used tool for model combination using Bayesian inference. Different versions of an expectation-maximisation (EM) algorithm are frequently used to apply BMA, typically in a homoscedastic context. In many situations, such as climate risk modelling or actuarial reserves, the homoscedasticity assumption does not hold. Moreover, the EM algorithm has the well-known issue of convergence to a single model. In this paper, we adapt the EM algorithm to a heteroscedastic context. We also propose a numerical error integration approach to address the problem of convergence. Finally, we generalise the proposed error integration approach by considering weights as a Dirichlet random variable, allowing for weights to vary. We compare the proposed approaches through simulation studies and a Property & Casualty insurance simulated dataset. We discuss some advantages of the proposed methods.

  • S.Jessup, M.Mailhot & M.Pigeon (2023), Impact of Combination Methods on Extreme Precipitation Projections, Annals of Actuarial Science, 1-20.

    Climate change is expected to increase the frequency and intensity of extreme weather events. In order to properly assess the increased economical risk of these events, actuaries can gain in relying on expert models/opinions from multiple different sources, which requires the use of model combination techniques. From non-parametric to Bayesian approaches, different methods rely on varying assumptions potentially leading to very different results. In this paper, we apply multiple model combination methods to an ensemble of 24 experts in a pooling approach and use the differences in outputs from the different combinations to illustrate how one can gain additional insight from using multiple methods. The densities obtained from pooling in Montreal and Quebec City highlight the significant changes in higher quantiles obtained through different combination approaches. Areal reduction factor (ARF) and quantile projected changes are used to show that consistency, or lack thereof, across approaches reflects the uncertainty of combination methods. This shows how an actuary using multiple expert models should consider more than one combination method in order to properly assess the impact of climate change on loss distributions, seeing as a single method can lead to overconfidence in projections.

  • S.Jessup, J.-P. Boucher & M.Pigeon (2020), On Fitting Dependent Nonhomogeneous Loss Models to Unearned Premium Risk, North American Actuarial Journal, 25(4), 524-542.

    Unearned premium, or more particularly the risk associated to it, has only recently received regulatory attention. Unearned losses occur after the evaluation date for policies written before the evaluation date. Given that an inadequate acquisition pattern of premium and approximate modelling of premium liability can lead to an inaccurate reserve around unearned premium risk, an individual nonhomogeneous loss model including cross-coverage dependence is proposed to provide an alternative method of evaluating this risk. Claim occurrence is analysed in terms of both claim seasonality and multiple coverage frequency. Homogeneous and heterogeneous distributions are fitted to marginals. Copulas are fitted to pairs of coverages using rank-based methods and a tail function. This approach is used on a recent Ontario auto database.

Présentations scientifiques

  • Robust Extreme Thresholds Through Generalised Bayesian Model Averaging, Congrès annuel de la Société statistique du Canada, St-John’s, Canada (TN), 2 juin 2024.
  • Uncertainty In Heteroscedastic Bayesian Model Averaging, Computational and Methodological Statistics (CMS) International Conference , Berlin, Allemagne, 16 décembre 2023.
  • Impact Of Combination Methods On Extreme Precipitation Projections, Actuarial Research Conference (ARC), Drake University, Des Moines, USA (IA), 30 juillet 2023.
  • On The Impact Of Model Combination Methods On Extreme Precipitation Projections, Congrès annuel de la Société statistique du Canada, Virtuel, 30 mai 2022.
  • Non-Homogeneous Loss Models Applied To Unearned Premium Risk, Actuarial Research Conference (ARC), Indianapolis, USA (IN), 14 août 2019.
  • Loss Reserving Models For The Unearned Premium Risk, Joint Statistical Meeting (JSM), Denver, USA (CO), 27 juillet 2019.

Implications

Présentations locales

  • Modèles de pertes non-homogènes avec dépendance pour le risque de prime non-acquise, 2e Atelier de la Chaire CARA , UQAM, Montréal, Canada (QC), 29 novembre 2019.

Enseignement

Démonstrations