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The standard IFRS 17 introduces a risk adjustment (RA) to reflect the compensation the insurance entity requires for bearing the uncertainty associated with nonfinancial risks. The risk adjustment is one of the main components in IFRS 17 disclosures and is a factor that impacts strongly IFRS 17 P&L and balance sheet as well as their evolution over a time horizon. IFRS 17 does not prescribe any specific techniques for calculation methodologies; insurance entities are free to adopt their own assessment while meeting several qualitative rules to ensure their consistency. This paper focuses on the recommendations of paragraph §B88 stating that the risk adjustment is required to reflect the diversification benefit of bearing the risk. We suggest a method for aggregating elementary RA (per risk and/or per Line of Business) based on the Solvency 2 elliptic aggregation. We introduce the concept of ultimate correlation as opposed to Solvency 2 one-year correlation and provide a theoretical bridge between both depending on a time diversification parameter. We explore correlation structures involving this time diversification and discuss analytical properties in terms of possible correlations values and the resulting impact on the aggregated RA features.

Marine hard-bottom communities are undergoing severe change under the influence of multiple drivers, notably climate change, extraction of natural resources, pollution and eutrophication, habitat degradation, and invasive species. Monitoring marine biodiversity in such habitats is, however, challenging as it typically involves expensive, non-standardized, and often destructive sampling methods that limit its scalability. Differences in monitoring approaches furthermore hinders inter-comparison among monitoring programs. Here, we announce a Marine Biodiversity Observation Network (MBON) consisting of Autonomous Reef Monitoring Structures (ARMS) with the aim to assess the status and changes in benthic fauna with genomic-based methods, notably DNA metabarcoding, in combination with image-based identifications. This article presents the results of a 30-month pilot phase in which we established an operational and geographically expansive ARMS-MBON. The network currently consists of 20 observatories distributed across European coastal waters and the polar regions, in which 134 ARMS have been deployed to date. Sampling takes place annually, either as short-term deployments during the summer or as long-term deployments starting in spring. The pilot phase was used to establish a common set of standards for field sampling, genetic analysis, data management, and legal compliance, which are presented here. We also tested the potential of ARMS for combining genetic and image-based identification methods in comparative studies of benthic diversity, as well as for detecting non-indigenous species. Results show that ARMS are suitable for monitoring hard-bottom environments as they provide genetic data that can be continuously enriched, re-analyzed, and integrated with conventional data to document benthic community composition and detect non-indigenous species. Finally, we provide guidelines to expand the network and present a sustainability plan as part of the European Marine Biological Resource Centre (www.embrc.eu). This ARMS-MBON network is funded by the infrastructure programs ASSEMBLE Plus (grant no. 730984) and the European Marine Biological Resource Centre, EMBRC. Both programs establish and maintain the core network and provide services and consultation for deployment, sample processing, sequencing, data management, and analysis. Funding for ARMS observatories in the North Sea Region was provided by the INTERREG project GEANS (North Sea Program of the European Regional Development Fund of the European Union) and the Swedish Agency for Marine and Water Management (grant no. 31812019), and the Flanders LifeWatch contribution (Research Foundation Flanders grant I000819N). The ARMS observatory in Roscoff also received support from the Aquanis 2.0 project (FONDATION Total). Data management and analysis was funded by Swedish LifeWatch grant from the Swedish Research council (grant no. 2017-00634) as well as the EOSC NORDIC project (grant no. 857652). Guiding documents to obtain ABS clearance for access to genetic resources were developed in the framework of projects INTERREG EBB (EAPA_501/2016) and H2020 EOSC-Life (grant no. 824087).

The so-called market-consistency of the European life insurance valuation as shaped by regulation guidelines embeds numerous theoretical and practical misstatements. Since El Karoui et al. (2017) the manipulation risk induced by the framework imprecision and, in particular, its high dependency to regulatory and non-regulatory calibration data is clear. In this paper we update some results and analysis of El Karoui et al. (2017) using data from a more recent "classical" year (2017) and from an exceptional year (first quarter of 2020, with Covid-19 effects), and test additional sensitivities. Based on the updated values we obtain up to-45% in the V IF estimates values depending on the swaption implied volatilities matrix used to calibrate the interest rates model. Then trying different calibration sets we obtain up to 105% difference. In parallel, we see that using 3-month averages to calibrate Economic Scenario Generators do not make effects of crises like Covid-19 disappear. We then address the "simulation seed" setting issue, and the interest and limits of keeping the same seed when estimating and comparing economic valuations, be it on horizontal (comparing valuations through time) or vertical (studying sensitivities at the same date) analysis. We finally open our study to propose various tools for a better risk management of economic scenarios and valuation, through a better understanding of Asset-Liability Management models.

This paper is concerned with the quantification of basis risk in index-based insurance products using randomly scaled variables. To this extent, we first discuss the shape, the unimodality and the symmetry of randomly scaled variables depending on the distribution of the random scaling factor using Mellin transform. We explicitly obtain the distribution of a randomly scaled variable when the random scaling factor is either uniformly distributed or of Beta type. We then determine s-convex extremal distributions for randomly scaled variables and discuss the way of comparing it. Next, we define an Enterprise Risk Management framework that relies on randomly scaled variables to assess basis risk, introducing the class of generalized penalty functions. This ERM framework allows for setting up basis risk limits to eventually determine a Basis Risk Capital Requirement. The results are illustrated with particular cases that carefully challenge the methodology.

This paper is concerned with properties of Beta-unimodal distributions and their use to assess the basis risk inherent to index-based insurance or reinsurance contracts. To this extent, we first characterize s-convex stochastic orders for Beta-unimodal distributions in terms of the Weyl fractional integral. We then determine s-convex extrema for such distributions , focusing in particular on the cases s = 2, 3, 4. Next, we define an Enterprise Risk Management framework that relies on Beta-unimodality to assess these hedge imperfections , introducing several penalty functions and worst case scenarios. Some of the results obtained are illustrated numerically via a representative catastrophe model.

On paper, prevention appears to be a good complement to health insurance. However, its implementation is often costly. To maximize the impact and efficiency of prevention plans these should target particular groups of policyholders. In this article, we propose a way of clustering policyholders that could be a starting point for the targeting of prevention plans. This two-step method mainly classifies using policyholder health consumption. This dimension is first reduced using a Nonnegative matrix factorization algorithm, producing intermediate health-product clusters. We then cluster using Kohonen's map algorithm. This leads to a natural visualization of the results, allowing the simple comparison of results from different databases. We apply our method to two real health-insurer datasets. We carry out a number of tests (including tests on a text-mining database) of method stability and clustering ability. The method is shown to be stable, easily-understandable, and able to cluster most policyholders efficiently.

This paper aims to shed light on the dilemma faced by insurance purchasers faced with multiple distribution channels. Should the consumer herself choose from a large set of insurance policies or rather delegate a part her decision to an intermediary who is more or less honest? We consider decisions based on a number of real-world insurance distribution channels with different information frames. Beliefs about intermediary honesty are the main determinants of individual choice. In addition, the obfuscation of information is the main source of inefficiency in decision-making, particularly regarding the characteristics of the insurance contracts chosen by consumers.

We consider the minimax quickest detection problem of an unobservable time of change in the rate of an inhomogeneous Poisson process. We seek a stopping rule that minimizes the robust Lorden criterion, formulated in terms of the number of events until detection, both for the worst-case delay and the false alarm constraint. In the Wiener case, such a problem has been solved using the so-called cumulative sums (cusum) strategy by Shiryaev [33, 35], or Moustakides [24] among others. In our setting, we derive the exact optimality of the cusum stopping rule by using finite variation calculus and elementary martingale properties to characterize the performance functions of the cusum stopping rule in terms of scale functions. These are solutions of some delayed differential equations that we solve elementarily. The case of detecting a decrease in the intensity is easy to study because the performance functions are continuous. In the case of an increase where the performance functions are not continuous, martingale properties require using a discontinuous local time. Nevertheless, from an identity relating the scale functions, the optimality of the cusum rule still holds. Finally, some numerical illustration are provided.

International audience; The purpose of this paper is to point out that an asymptotic rule "A+B/u" for the ultimate ruin probability applies to a wide class of dependent risk models, in discrete and continuous time. Dependence is incorporated through a mixing approach among claim amounts or claim inter-arrival times, leading to a systemic risk behavior. Ruin corresponds here either to classical ruin, or to stopping the activity after realizing that it is not pro table at all, when one has little possibility to increase premium income rate. Several special cases for which closed formulas are derived, are also investigated in some detail.

Ce document pr\ésente une synthèse de mes travaux sur des problématiques de mathématiques appliquées à l'actuariat. La théorie du risque, également appelée théorie de la ruine, concerne d'une manière générale l'évaluation de probabilités de réalisations d'événements défavorables pour des compagnies d'assurances. Au-delà de ces calculs de probabilités dans un modèle fixé, des branches de cette théorie s'intéressent aussi à différents problèmes d'optimisation: d'allocation de réserve, de stratégie de versement de dividendes ou d'imposition (au sens de la fiscalité), d'investissement dans des actifs risqués, de programme de réassurance...

We explain why correlation crises may occur in insurance and finance. These phenomena are not taken into account in Solvency II standard formula. We show the importance of taking them into account in internal models or partial internal models. Given the variety of scenarios that could lead to correlation crises and their different potential impacts, we support the idea that ORSA (Own Risk and Solvency Assessment) reports of insurance companies should include dynamic and causal correlation crises analyzes.

Arthur Charpentier (see Arthur's blog) was recently contacted by some researchers willing to test if a multivariate copula is - or not - Gaussian. They use a test proposed in Malevergne and Sornette (2003) stating that one should simply test for pairwise normality. This test may be of importance in finance, in actuarial science, and in risk management in general: for example, given 120 financial assets, in order to test whether or not some 120-dimensional random vector of interest in finance admits a Gaussian copula, can one restrict the Gaussian copula hypothesis test to pairs of assets? This short note proves that it is not the case, and provides a simple counter-example based on some multivariate EFGM copula. This confirms the intuition that one cannot only consider all pairs of the studied random variables and that one cannot avoid to study the full vector to test whether a random vector admits a Gaussian copula. An earlier counter-example, discovered after writing this note, is also mentioned.

In the renewal risk model, several strong hypotheses may be found too restrictive to model accurately the complex evolution of the reserves of an insurance company. In the case where claim sizes are heavy-tailed, we relax independence and stationarity assumptions and extend some asymptotic results on finite-time ruin probabilities, to take into account possible correlation crises like the one recently bred by the sub-prime crisis: claim amounts, in general assumed to be independent, may suddenly become strongly positively dependent. The impact of dependence and non-stationarity is analyzed and several concrete examples are given.

In most stochastic mortality models, either one stochastic intensity process (for example a jump-diffusion process) or a collection of independent processes is used to model the stochastic evolution of survival probabilities. We propose and calibrate a new model that takes inter-age correlations into account. The so-called stochastic logit's Deltas model is based on the study of the multivariate time series of the differences of logits of yearly mortality rates. These correlations are important and we illustrate our study on a real-life portfolio. We determine their impact on the price of a longevity swap type reinsurance contract, in which most of the financial risk is taken by a third party. The hypotheses of our model are statistically tested and various measures of risk of the present value of liabilities are found to be significantly smaller in our model than in the case of one common underlying stochastic process.

International audience; En Assurance Vie, certaines caractéristiques de contrats jouent un rôle majeur dans la décision de l'assuré de racheter son contrat. Les conditions de souscription, son âge, sa profession ainsi que d'autres facteurs propres à sa situation lors de la souscription influencent ses décisions. Il est également possible que l'environnement économique et financier soit important. Deux modèles de segmentation nous ont permis de développer ces idées : les arbres de classification et de régression, et la régression logistique. Les contrats de type Prévoyance ainsi que ceux d'Epargne sont impactés, et les résultats montrent clairement que la garantie de participation au bénéfice est très discriminante. Nous nous focalisons dans cette étude sur des produits de type Mixte. Nous présentons dans un premier temps les fondamentaux de chacun des modèles ainsi que leurs hypothèses et limites. Puis nous testons différents facteurs comme possibles déclencheurs de la décision de rachat, dans le but de segmenter le portefeuille en classe de risque : la duration du contrat et l'option de participation au bénéfice sont des éléments essentiels. En dernière partie, nous discutons des différences entre les deux modélisations en termes de résultats numériques et d'un point de vue opérationnel.

International audience; For general risk processes, the expected time-integrated negative part of the process on a fixed time interval is introduced and studied. Differentiation theorems are stated and proved. They make it possible to derive the expected value of this risk measure, and to link it with the average total time below zero studied by Dos Reis (1993) and the probability of ruin. Differentiation of other functionals of unidimensional and multidimensional risk processes with respect to the initial reserve level are carried out. Applications to ruin theory, and to the determination of the optimal allocation of the global initial reserve which minimizes one of these risk measures, illustrate the variety of application fields and the benefits deriving from an efficient and effective use of such tools.