Michel Denuit's research while affiliated with Université Libre de Bruxelles and other places

... Property BT is sometimes argued as an undesirable property; see Denuit et al. (2022b). We give a simple example below for the purpose of discussion. ...

... As an important risk sharing rule in economic theory with many attractive properties, CMRS was used by Landsberger and Meilijson (1994) to study Pareto optimality of comonotonic risk allocations, and its properties were studied in detail by Denuit and Dhaene (2012); see Denuit et al. (2022a) for a summary of its properties. Our characterization hence provides a first axiomatic foundation for CMRS and its applications in economic theory and decentralized finance and insur-1 See the later work on risk sharing by Barrieu and El Karoui (2005) for convex risk measures, Carlier et al. (2012) for stochastic dominance, Xia and Zhou (2016) for rank-dependent utilities, Cai et al. (2017) for reinsurance arrangements, and Embrechts et al. (2018) for quantile-based risk measures. ...

... Denuit (2020) derived formulas for the tail conditional expectations (TCE) of some univariate compound distributions. Denuit and Robert (2021) presented some results for the TCE of a compound mixed Poisson model, where both the claim frequencies and sizes depend on several latent variables. Ren (2021) derived the formulas for the TCE and tail variance (TV) of multivariate compound models based on Sundt (1999), where claim frequency is one-dimensional and one claim can yield multiple dependent losses. ...

... To facilitate rate regulation, variable selections or variable importance measures associated with linear models are much more accessible to conduct than non-linear models such as neural networks or decision-tree-based methods. The machine learning models often outperform GLM or other linear models [15][16][17], but they are considered to be black box models and may create obstacles in communication among the fields associated with the regulatory practice. This helps to answer why, in rate regulation, regulators are reluctant to use machine learning models to estimate relativities of major risk factors, which are served as benchmark values for auto insurance companies. ...

... Remark that we do not strictly distinguish between prior and posterior information, here. If we go over to a time-series consideration, where more and more claims experience becomes available of an individual driver, we should clearly distinguish the different sets of information, because otherwise it may happen that in prior and posterior pricing factors we correct twice for the same factor; an interesting paper is Corradin et al. [82]. ...

... Turning to risk sharing, Denuit (2019) linked size-biased transform to individual allocations resulting from the application of the conditional mean risk sharing rule proposed by Denuit and Dhaene (2012). Properties of this risk sharing rule have been obtained by exploiting its relationship with size-biasing in Denuit and Robert (2020a), Denuit and Robert (2020b), Denuit and Robert (2021a), Denuit and Robert (2021b), and Denuit (2021c). The multivariate version of the size-biased transform we use to deal with correlated losses is a particular case of the one proposed in Furman and Zitikis (2007) and Furman et al. (2021a) and Furman et al. (2021b). ...

... Furthermore, in their paper, Denuit and Robert (2021) studied three insurance business models: carrier, broker, and self-governing. In the current paper, the author proposed an actuarial based model on 'conditional mean risk sharing', This paper aims to formalize the three business models dominating peer-to-peer (P2P) property and casualty insurance: self-governing, broker, and carrier. ...