Michel Denuit’s research while affiliated with Catholic University of Louvain and other places

This work presents a framework for peer-to-peer (P2P) basis risk management applied to solar electricity generation. The approach leverages physically based simulation models to estimate the day-ahead production forecasts and the actual realized production at the solar farm level. We quantify the financial loss from mismatches between forecasted and actual production using the outputs of these simulations. The framework then implements a parametric insurance mechanism to mitigate these financial losses and combines it with a P2P market structure to enhance participant risk sharing. By integrating day-ahead forecasts and actual production data with physical modeling, this method provides a comprehensive solution to manage production variability, offering practical insights for improving financial resilience in renewable energy systems. The results highlight the potential of combining parametric insurance with P2P mechanisms to foster reliability and collaboration in renewable energy markets.

The conditional expectation $m_{X}(s)=\mathrm{E}[X|S=s]$ , where X and Y are two independent random variables with S=X+Y , plays a key role in various actuarial applications. For instance, considering the conditional mean risk-sharing rule, $m_X(s)$ determines the contribution of the agent holding the risk X to a risk-sharing pool. It is also a relevant function in the context of risk management, for example, when considering natural capital allocation principles. The monotonicity of $m_X(\!\cdot\!)$ is particularly significant under these frameworks, and it has been linked to log-concave densities since Efron (1965). However, the log-concavity assumption may not be realistic in some applications because it excludes heavy-tailed distributions. We consider random variables with regularly varying densities to illustrate how heavy tails can lead to a nonmonotonic behavior for $m_X(\!\cdot\!)$ . This paper first aims to identify situations where $m_X(\!\cdot\!)$ could fail to be increasing according to the tail heaviness of X and Y . Second, the paper aims to study the asymptotic behavior of $m_X(s)$ as the value s of the sum gets large. The analysis is then extended to zero-augmented probability distributions, commonly encountered in applications to insurance, and to sums of more than two random variables and to two random variables with a Farlie–Gumbel–Morgenstern copula. Consequences for risk sharing and capital allocation are discussed. Many numerical examples illustrate the results.

This note revisits Simpson’s paradox and discusses confounding effects of hidden covariates on Kendall’s tau. As a result, observed correlation may vanish or even revert. More specifically, a decomposition of Kendall’s tau in the presence of subgroups is established, a formal definition of Simpson’s paradox for Kendall’s tau is given and some simple examples of paradoxical situations in the insurance domain are provided. Finally, necessary and sufficient conditions for a Simpson’s paradox to occur are studied.

Soetewey et al. (Eur Actuar J 11(1):135–160, 2021) proposed to determine the waiting period opening the right to be forgotten (RTBF) as the time after diagnosis needed for the premium to revert back to some acceptable level expressed by means of regulatory life tables. However, this approach requires data up to 30 years after diagnosis (10 years of standard RTBF plus the typical duration of the loan), or extrapolating the results up to that time horizon. When survival statistics are only available over a shorter duration, it turns out that the results may strongly depend on the extrapolation method. This is why an alternative method is proposed here, based on a constraint imposed to the premium. This constraint is then transposed into a target on the conditional observed survival and the waiting period follows. For the sake of robustness, results obtained with the proposed approach are compared to results obtained with Kaplan–Meier estimate taken as a non-parametric reference. Furthermore, the paper investigates the impact of the stage of the tumor at diagnosis on waiting periods.

This paper considers a risk sharing scheme of independent discrete losses that combines risk retention at individual level, risk transfer for too expensive losses and risk pooling for the middle layer. This ensures that pooled losses can be considered as being uniformly bounded. We study the no-sabotage requirement and diversification effects when the conditional mean risk-sharing rule is applied to allocate pooled losses. The no-sabotage requirement is equivalent to Efron’s monotonicity property for conditional expectations, which is known to hold under log-concavity. Elementary proofs of this result for discrete losses are provided for finite population pools. The no-sabotage requirement and diversification effects are then examined within large pools. It is shown that Efron’s monotonicity property holds asymptotically and that risk can be eliminated under fairly general conditions which are fulfilled in applications.