Projets de recherche

J.-P. Boucher, R.Coulibaly & J. Trufin (2025), Varying Risk Exposure in Auto Insurance: A Weighted Tweedie Framework for Experience Rating and Cancellation Penalties,

This paper develops a weighted Tweedie regression framework to model early policy cancellations in auto insurance, with a focus on the interplay between experience rating, fairness, and penalty structures. Traditional Tweedie models are extended through weighted likelihoods to better capture heterogeneous risk exposures and the varying credibility of policyholder histories. Building on the theory of auto-calibration and stochastic orders, we analyze how cancellation behavior departs from classical risk-based pricing and how it can be incorporated into predictive models. The framework allows insurers to account for the dual objectives of financial stability and social fairness by explicitly modeling cancellation risk alongside claim costs. Empirical results on auto insurance telematics data illustrate how weighted Tweedie models can detect systematic biases in standard experience rating, identify optimal penalty schemes, and ensure coherent alignment between risk exposure, predictive accuracy, and equitable treatment of policyholders. This approach offers a principled method to balance actuarial soundness with policyholder retention and regulatory considerations.

S.Jessup, M.Mailhot & M.Pigeon (2025), Flexible extreme thresholds through generalised Bayesian model averaging,

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.

R.Turcotte & P. Shi (2025), Individual Loss Reserving for Multi-coverage Insurance,

Individual loss reserving methods have undergone substantial development in the past decade, driven by increased accessibility to granular-level insurance claims data. This paper presents a micro loss reserving model tailored for multi-coverage insurance policies, where a single insurance claim might trigger payments from multiple coverage types. We employ a copula-based multivariate regression approach to jointly model the settlement time and loss amount, effectively capturing the dependence among various types of loss amounts and their correlation with the settlement time. We stress the importance of considering both types of dependence for accurate reserving prediction and uncertainty quantification. Furthermore, we propose computationally efficient algorithms for parameter estimation and dynamic prediction. Through numerical experiments and real data analysis, we demonstrate the effectiveness of our proposed multivariate predictive model in loss reserving applications.

A.O.Chuisseu Tchuisseu, E.Marceau, H.Cossette & J.-P. Boucher (2025), Actuarial fire-spreading model based on tree-structured graphical models,

In this paper, we propose a general framework to model fire propagation in spatially connected environments, such as adjacent buildings or interconnected rooms within a single dwelling. Each such environment is represented as a tree-like structure, where units (e.g., rooms or substructures) are connected by edges that reflect potential paths for fire spread. Our analysis considers tree-structured sites with up to five units. Since the cases with one, two, and three units are straightforward, we focus on the more intricate configurations with four and five units. For each configuration, we provide a stochastic representation of the total fire losses and analyze the effect of probabilities of propagation using stochastic orders. The investigation compares various tree structures by employing the stop-loss order to highlight differences in risk profiles between them. The model is further examined through a numerical application, offering insights into practical implications for insurance, particularly in calculating premiums and risk measures. Our approach provides a comprehensive tool for assessing fire risk in complex structural layouts, with analytical advantages over simulation-based methods.

I.Kouarfate, A.Mackay & M.Pigeon (2025), Hybrid Decision Tree for Individual Reserve Modeling in P&C Insurance,

Once technology matures, quantum computers are expected to solve certain problems much faster than classical computers. The potential applications of quantum computing are numerous, and quantum finance is an emerging research field that is generating strong interest from both academia and industry. In this context, it is essential to study how quantum computing can be applied in the insurance sector. Property and Casualty (P&C) insurance companies face high volatility due to the uncertain nature of claims they must cover. Regulations therefore require them to maintain reserves to ensure solvency up to a given risk level. Over the past twenty years, individual reserving approaches have been widely studied in the literature and gradually adopted by insurers to evaluate the required level of reserves. Many of these methods rely on statistical learning and present significant computational challenges. In this project, we focus on approaches based on binary decision trees. We propose hybrid (classical/quantum) implementation of a decision tree for individual claim reserving. To reduce the computational burden caused by the presence of many categorical explanatory variables, we will use the representation of binary classification trees with binary features as quantum circuits proposed by [HEE22]. To ensure the reproducibility of results, we will first work with simulated data before applying the method to real insurance data.

J.-P. Boucher & R.Coulibaly (2025), Comparison of Offset and Ratio Weighted Regressions in Tweedie Models with Application to Mid-Term Cancellations,

In property and casualty insurance, particularly in automobile insurance, risk exposure is traditionally associated with the coverage duration. However, factors such as early contract cancellations demand more precise modelling to ensure accurate premium pricing. This study introduces and compares two approaches for modelling total claims (or loss costs) in insurance portfolios with a high proportion of policies that have partial-year exposure: the offset and ratio methods. We demonstrate that both approaches can be viewed as weighted regressions under the Tweedie distribution framework. Through an analysis based on the financial balance property, we find that the ratio approach outperforms the offset method. This comparison is illustrated using an automobile insurance portfolio, where a significant share of policyholders terminate their contracts before the coverage period concludes.

M.Michaelides, H.Cossette & M.Pigeon (2024), Parametric estimation of conditional Archimedean copula generators for censored data,

In this paper, we propose a novel approach for estimating Archimedean copula generators in a conditional setting, incorporating endogenous variables. Our method allows for the evaluation of the impact of the different levels of covariates on both the strength and shape of dependence by directly estimating the generator function rather than the copula itself. As such, we contribute to relaxing the simplifying assumption inherent in traditional copula modeling. We demonstrate the effectiveness of our methodology through applications in two diverse settings: a diabetic retinopathy study and a claims reserving analysis. In both cases, we show how considering the influence of covariates enables a more accurate capture of the underlying dependence structure in the data, thus enhancing the applicability of copula models, particularly in actuarial contexts.