arXiv subjects

Michel Denuit

Publications and source records attributed to Michel Denuit.

5 recordsLinked to original sources

arXiv2026

Linear Risk Sharing in Community-Based Insurance: Ruin Reduction in the Compound Poisson Model

This paper studies proportional risk sharing at claim occurrence time in community-based insurance. Each participant is modeled by an individual Cram\'er-Lundberg surplus process, and, whenever a claim is reported within the pool, its cost is redistributed according to a fixed allocation matrix. We compare the infinite-time ruin probability of each participant under stand-alone operation and under pool participation. Our main result shows that pooling reduces, for every participant, the infinite-time ruin probability when claim severities belong to a common scale family, the allocation rule satisfies full allocation and actuarial fairness, and each transfer remains bounded by an individual capacity condition. The proof relies on a convex-order comparison between the losses borne inside the pool and the corresponding stand-alone losses. We also clarify the role of these assumptions by showing that, outside this framework, pooling need not be beneficial for all participants. Numerical illustrations with Exponential and LogNormal severities support the theoretical findings and highlight how the design of proportional sharing rules affects solvency. The paper thus provides simple and interpretable sufficient conditions under which transparent linear risk-sharing arrangements improve individual solvency in community-based insurance.

math.PR↗

arXiv2026

Balance and Fairness through Multicalibration in Nonlife Insurance Pricing

Autocalibration is known to be an important requirement for insurance premiums since it guarantees that premium income balances corresponding claims, on average, not only at portfolio level but also inside each group paying similar premiums. Also, fairness has become a major concern because unfair treatment may expose insurers to lawsuits or reputational damage. Translating fairness into conditional mean independence allows actuaries to combine autocalibration and fairness into the multicalibration concept. This paper studies the properties of multicalibration in an insurance context and proposes practical ways to implement it, through local regression or bias correction within groups including credibility adjustments. A case study based on motor insurance data illustrates the relevance of multicalibration in insurance pricing.

stat.OT↗

arXiv2025

Peer-to-Peer Basis Risk Management for Renewable Production Parametric Insurance

The financial viability of renewable energy projects is challenged by the variability and unpredictability of production due to weather fluctuations. This paper proposes a novel risk management framework combining parametric insurance and peer-to-peer (P2P) risk sharing to address production uncertainty in solar electricity generation. We first design a weather-based parametric insurance scheme to protect against forecast errors, recalibrated at the site level to mitigate geographical basis risk. To handle residual mismatches between insurance payouts and actual losses, we introduce a complementary P2P mechanism that redistributes the remaining basis risk among participants. The method leverages physically based simulation models to reconstruct day-ahead forecasts and realized productions, integrating climate data and solar farm characteristics. A second-order theoretical approximation links heterogeneous local models to a shared weather index, making risk sharing operationally feasible. In an empirical application to 50 German solar farms, our approach reduces the volatility of production losses by 55\%, demonstrating its potential to stabilize revenues and strengthen the resilience of renewable investments.

stat.AP↗

arXiv2021

Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning

Boosting techniques and neural networks are particularly effective machine learning methods for insurance pricing. Often in practice, there are nevertheless endless debates about the choice of the right loss function to be used to train the machine learning model, as well as about the appropriate metric to assess the performances of competing models. Also, the sum of fitted values can depart from the observed totals to a large extent and this often confuses actuarial analysts. The lack of balance inherent to training models by minimizing deviance outside the familiar GLM with canonical link setting has been empirically documented in Wüthrich (2019, 2020) who attributes it to the early stopping rule in gradient descent methods for model fitting. The present paper aims to further study this phenomenon when learning proceeds by minimizing Tweedie deviance. It is shown that minimizing deviance involves a trade-off between the integral of weighted differences of lower partial moments and the bias measured on a specific scale. Autocalibration is then proposed as a remedy. This new method to correct for bias adds an extra local GLM step to the analysis. Theoretically, it is shown that it implements the autocalibration concept in pure premium calculation and ensures that balance also holds on a local scale, not only at portfolio level as with existing bias-correction techniques. The convex order appears to be the natural tool to compare competing models, putting a new light on the diagnostic graphs and associated metrics proposed by Denuit et al. (2019).

stat.ML↗

arXiv2014

Max-factor individual risk models with application to credit portfolios

Individual risk models need to capture possible correlations as failing to do so typically results in an underestimation of extreme quantiles of the aggregate loss. Such dependence modelling is particularly important for managing credit risk, for instance, where joint defaults are a major cause of concern. Often, the dependence between the individual loss occurrence indicators is driven by a small number of unobservable factors. Conditional loss probabilities are then expressed as monotone functions of linear combinations of these hidden factors. However, combining the factors in a linear way allows for some compensation between them. Such diversification effects are not always desirable and this is why the present work proposes a new model replacing linear combinations with maxima. These max-factor models give more insight into which of the factors is dominant.

stat.ME↗