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1. Predicted Impacts of Booster, Immunity Decline, Vaccination Strategies, and Non-Pharmaceutical Interventions on COVID-19 Outcomes in France

Author

Simon Pageaud, Anne Eyraud-Loisel, Jean-Pierre Bertoglio, Alexis Bienvenüe, Nicolas Leboisne, Catherine Pothier, Christophe Rigotti, Nicolas Ponthus, Romain Gauchon, François Gueyffier, Philippe Vanhems, Jean Iwaz, Stéphane Loisel, Pascal Roy, and on behalf of the CovDyn Group (Covid Dynamics)

Subjects
vaccination, COVID-19, agent-based model, decision support techniques, booster, Medicine
Abstract

The major economic and health consequences of COVID-19 called for various protective measures and mass vaccination campaigns. A previsional model was used to predict the future impacts of various measure combinations on COVID-19 mortality over a 400-day period in France. Calibrated on previous national hospitalization and mortality data, an agent-based epidemiological model was used to predict individual and combined effects of booster doses, vaccination of refractory adults, and vaccination of children, according to infection severity, immunity waning, and graded non-pharmaceutical interventions (NPIs). Assuming a 1.5 hospitalization hazard ratio and rapid immunity waning, booster doses would reduce COVID-19-related deaths by 50–70% with intensive NPIs and 93% with moderate NPIs. Vaccination of initially-refractory adults or children ≥5 years would half the number of deaths whatever the infection severity or degree of immunity waning. Assuming a 1.5 hospitalization hazard ratio, rapid immunity waning, moderate NPIs and booster doses, vaccinating children ≥12 years, ≥5 years, and ≥6 months would result in 6212, 3084, and 3018 deaths, respectively (vs. 87,552, 64,002, and 48,954 deaths without booster, respectively). In the same conditions, deaths would be 2696 if all adults and children ≥12 years were vaccinated and 2606 if all adults and children ≥6 months were vaccinated (vs. 11,404 and 3624 without booster, respectively). The model dealt successfully with single measures or complex combinations. It can help choosing them according to future epidemic features, vaccination extensions, and population immune status.

Published
2022
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2. Expected Evolution of COVID-19 Epidemic in France for Several Combinations of Vaccination Strategies and Barrier Measures

Author

Simon Pageaud, Catherine Pothier, Christophe Rigotti, Anne Eyraud-Loisel, Jean-Pierre Bertoglio, Alexis Bienvenüe, Nicolas Leboisne, Nicolas Ponthus, Romain Gauchon, François Gueyffier, Philippe Vanhems, Jean Iwaz, Stéphane Loisel, Pascal Roy, and on behalf of the Group CovDyn (Covid Dynamics)

Subjects
vaccination, COVID-19, agent-based model, decision support techniques, Medicine
Abstract

The outbreak of the SARS-CoV-2 virus, enhanced by rapid spreads of variants, has caused a major international health crisis, with serious public health and economic consequences. An agent-based model was designed to simulate the evolution of the epidemic in France over 2021 and the first six months of 2022. The study compares the efficiencies of four theoretical vaccination campaigns (over 6, 9, 12, and 18 months), combined with various non-pharmaceutical interventions. In France, with the emergence of the Alpha variant, without vaccination and despite strict barrier measures, more than 600,000 deaths would be observed. An efficient vaccination campaign (i.e., total coverage of the French population) over six months would divide the death toll by 10. A vaccination campaign of 12, instead of 6, months would slightly increase the disease-related mortality (+6%) but require a 77% increase in ICU bed–days. A campaign over 18 months would increase the disease-related mortality by 17% and require a 244% increase in ICU bed–days. Thus, it seems mandatory to vaccinate the highest possible percentage of the population within 12, or better yet, 9 months. The race against the epidemic and virus variants is really a matter of vaccination strategy.

Published
2021
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5. Adapting French COVID-19 vaccination campaign duration to variant dissemination

Author

Pascal Roy, Catherine Pothier, Anne Eyraud-Loisel, Nicolas Ponthus, Philippe Vanhems, Simon Pageaud, Jean-Pierre Bertoglio, Alexis Bienvenüe, Nicolas Leboisne, Romain Gauchon, François Gueyffier, Jean Iwaz, Christophe Rigotti, Stéphane Loisel, Hospices Civils de Lyon (HCL), Laboratoire de Biométrie et Biologie Evolutive - UMR 5558 (LBBE), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Tribologie et Dynamique des Systèmes (LTDS), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-École Nationale des Travaux Publics de l'État (ENTPE)-Ecole Nationale d'Ingénieurs de Saint Etienne-Centre National de la Recherche Scientifique (CNRS), Université de Lyon, Extraction de Caractéristiques et Identification (imagine), Laboratoire d'InfoRmatique en Image et Systèmes d'information (LIRIS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École Centrale de Lyon (ECL), Université de Lyon-Université Lumière - Lyon 2 (UL2)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Université Lumière - Lyon 2 (UL2), Data Mining and Machine Learning (DM2L), Artificial Evolution and Computational Biology (BEAGLE), Université de Lyon-Université Lumière - Lyon 2 (UL2)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Biométrie et Biologie Evolutive - UMR 5558 (LBBE), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mecanique des Fluides et d'Acoustique (LMFA), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Centre International de Recherche en Infectiologie - UMR (CIRI), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Université Lyon 1, Ecole Centrale de Lyon, INSA Lyon, Université de Lyon-Université de Lyon-École Nationale des Travaux Publics de l'État (ENTPE)-Ecole Nationale d'Ingénieurs de Saint Etienne (ENISE)-Centre National de la Recherche Scientifique (CNRS), Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Centre International de Recherche en Infectiologie (CIRI), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Université Jean Monnet - Saint-Étienne (UJM)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), and Rigotti, Christophe

Subjects
0303 health sciences, medicine.medical_specialty, education.field_of_study, business.industry, Public health, Population, Outbreak, International health, Disease, 3. Good health, Vaccination, 03 medical and health sciences, 0302 clinical medicine, [SDV.SPEE] Life Sciences [q-bio]/Santé publique et épidémiologie, Intensive care, Pandemic, medicine, [SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie, 030212 general & internal medicine, business, education, 030304 developmental biology, Demography
Abstract

BackgroundThe outbreak of SARS-CoV-2 virus has caused a major international health crisis with serious consequences in terms of public health and economy. In France, two lockdown periods were decided in 2020 to avoid the saturation of intensive care units (ICU) and an increase in mortality. The rapid dissemination of variant SARS-CoV-2 VOC 202012/01 has strongly influenced the course of the epidemic. Vaccines have been rapidly developed. Their efficacy against the severe forms of the disease has been established, and their efficacy against disease transmission is under evaluation. The aim of this paper is to compare the efficacy of several vaccination strategies in the presence of variants in controlling the COVID-19 epidemic through population immunity.MethodsAn agent-based model was designed to simulate with different scenarios the evolution of COVID-19 pandemic in France over 2021 and 2022. The simulations were carried out ignoring the occurrence of variants then taking into account their diffusion over time. The expected effects of three Non-Pharmaceutical Interventions (Relaxed-NPI, Intensive-NPI, and Extended-NPI) to limit the epidemic extension were compared. The expected efficacy of vaccines were the values recently estimated in preventing severe forms of the disease (75% and 94%) for the current used vaccines in France (Pfizer-BioNTech and Moderna since January 11, 2021, and AstraZeneca since February 2, 2021). All vaccination campaigns reproduced an advanced age-based priority advised by the Haute Autorité de Santé. Putative reductions of virus transmission were fixed at 0, 50, 75 and 90%. The effects of four vaccination campaign durations (6-month, 12-month, 18-month and 24-month) were compared.ResultsIn the absence of vaccination, the presence of variants led to reject the Relaxed-NPI because of a high expected number of deaths (170 to 210 thousands) and the significant overload of ICUs from which 35 thousand patients would be deprived. In comparison with the situation without vaccination, the number of deaths was divided by 7 without ICU saturation with a 6-month vaccination campaign. A 12-month campaign would divide the number of death by 3 with Intensive-NPI and by 6 with Extended-NPI (the latter being necessary to avoid ICU saturation). With 18-month and 24-month vaccination campaigns without Extended-NPI, the number of deaths and ICU admissions would explode.ConclusionAmong the four compared strategies the 6-month vaccination campaign seems to be the best response to changes in the dynamics of the epidemic due to the variants. The race against the COVID-19 epidemic is a race of vaccination strategy. Any further vaccination delay would increase the need of strengthened measures such as Extended-NPI to limit the number of deaths and avoid ICU saturation.

Published
2021

6. Lessons learnt from the use of compartmental models over the COVID-19 induced lockdown in France

Author

Alexis Bienvenüe, Stéphane Derrode, Anne Eyraud-Loisel, Simon Pageaud, Pascal Roy, Romain Gauchon, Jean-Pierre Bertoglio, Jean Iwaz, Christophe Rigotti, Nicolas Ponthus, Stéphane Loisel, Pierre-Olivier Goffard, Vitaly Volpert, Catherine Pothier, Laboratoire de Sciences Actuarielle et Financière (SAF), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Laboratoire de Tribologie et Dynamique des Systèmes (LTDS), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-École Nationale des Travaux Publics de l'État (ENTPE)-Ecole Nationale d'Ingénieurs de Saint Etienne-Centre National de la Recherche Scientifique (CNRS), Extraction de Caractéristiques et Identification (imagine), Laboratoire d'InfoRmatique en Image et Systèmes d'information (LIRIS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École Centrale de Lyon (ECL), Université de Lyon-Université Lumière - Lyon 2 (UL2)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Université Lumière - Lyon 2 (UL2), Data Mining and Machine Learning (DM2L), Artificial Evolution and Computational Biology (BEAGLE), Université de Lyon-Université Lumière - Lyon 2 (UL2)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Biométrie et Biologie Evolutive - UMR 5558 (LBBE), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS), Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA), Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan [Villeurbanne] (ICJ), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mecanique des Fluides et d'Acoustique (LMFA), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Biométrie et Biologie Evolutive - UMR 5558 (LBBE), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS), Hospices Civils de Lyon (HCL), Université Lyon 1, Ecole Centrale de Lyon, INSA Lyon, Rigotti, Christophe, Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire d'InfoRmatique en Image et Systèmes d'information (LIRIS), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Université de Lyon-Université de Lyon-École Nationale des Travaux Publics de l'État (ENTPE)-Ecole Nationale d'Ingénieurs de Saint Etienne (ENISE)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), and Institut Camille Jordan (ICJ)

Subjects
infection dynamics, 0303 health sciences, education.field_of_study, Coronavirus disease 2019 (COVID-19), Calibration (statistics), prevalence, Population, Epidemic dynamics, COVID-19, Common framework, 3. Good health, 03 medical and health sciences, 0302 clinical medicine, Geography, [SDV.SPEE] Life Sciences [q-bio]/Santé publique et épidémiologie, Statistics, Prevalence studies, [SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie, Infection dynamics, 030212 general & internal medicine, Scale (map), education, compartmental model, 030304 developmental biology
Abstract

BackgroundCompartmental models help making public health decisions. They were used during the COVID-19 outbreak to estimate the reproduction numbers and predict the number of hospital beds required. This study examined the ability of closely related compartmental models to reflect equivalent epidemic dynamics.MethodsThe study considered three independently designed compartmental models that described the COVID-19 outbreak in France. Model compartments and parameters were expressed in a common framework and models were calibrated using the same hospitalization data from two official public databases. The calibration procedure was repeated over three different periods to compare model abilities to: i) fit over the whole lockdown; ii) predict the course of the epidemic during the lockdown; and, iii) provide profiles to predict hospitalization prevalence after lockdown. The study considered national and regional coverages.ResultsThe three models were all flexible enough to match real hospitalization data during the lockdown, but the numbers of cases in the other compartments differed. The three models failed to predict reliably the number of hospitalizations after the fitting periods at national as at regional scales. At the national scale, an improved calibration led to epidemic course profiles that reflected hospitalization dynamics and reproduction numbers that were coherent with official and literature estimates.ConclusionThis study shows that prevalence data are needed to further refine the calibration and make a selection between still divergent models. This underlines strongly the need for repeated prevalence studies on representative population samples.

Published
2021
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7. Likelihood Inference for Multivariate Extreme Value Distributions Whose Spectral Vectors have known Conditional Distributions

Author

Alexis Bienvenüe and Christian Y. Robert

Subjects
Statistics and Probability, Multivariate statistics, Multivariate random variable, 05 social sciences, Statistical parameter, 01 natural sciences, Normal-Wishart distribution, 010104 statistics & probability, Sampling distribution, 0502 economics and business, Statistics, Generalized extreme value distribution, Applied mathematics, Multivariate t-distribution, 0101 mathematics, Statistics, Probability and Uncertainty, 050205 econometrics, Mathematics, Multivariate stable distribution
Abstract

Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail dependence. The main approaches to inference for multivariate extremes consist in approximating either the distribution of block component-wise maxima or the distribution of the exceedances over a high threshold. Although the expressions of the asymptotic density functions of these distributions may be characterized, they cannot be computed in general. In this paper, we study the case where the spectral random vector of the multivariate max-stable distribution has known conditional distributions. The asymptotic density functions of the multivariate extreme value distributions may then be written through univariate integrals that are easily computed or simulated. The asymptotic properties of two likelihood estimators are presented, and the utility of the method is examined via simulation.

Published
2016
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8. Systemic Tail Risk Distribution

Author

Christian Yann Robert, Alexis Bienvenüe, Robert, Christian, Laboratoire de Sciences Actuarielle et Financière (SAF), Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon-Université de Lyon

Subjects
[QFIN.ST] Quantitative Finance [q-fin]/Statistical Finance [q-fin.ST], [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [QFIN.CP] Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], [QFIN.RM] Quantitative Finance [q-fin]/Risk Management [q-fin.RM], [QFIN.RM]Quantitative Finance [q-fin]/Risk Management [q-fin.RM], [QFIN.ST]Quantitative Finance [q-fin]/Statistical Finance [q-fin.ST], [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2016

9. Un principe d'invariance pour un algorithme génétique en population finie

Author

Jean Bérard and Alexis Bienvenüe

Subjects
General Medicine, Humanities, Mathematics
Abstract

Resume Nous etudions le comportement asymptotique d'un algorithme genetique de mutation-selection en population finie, defini sur les entiers et associe a une marche au hasard simple et a la fonction d'adaptation f ( x )= x . Nous prouvons un principe d'invariance pour le nuage de particules normalise.

Published
2000
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10. Un principe d'invariance pour une classe de marches p-corrélées sur ℤd

Author

Alexis Bienvenüe, Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon

Subjects
Statistics and Probability, [SHS.STAT]Humanities and Social Sciences/Methods and statistics, Markov chain, Characteristic function (probability theory), Function space, Covariance matrix, General Mathematics, 010102 general mathematics, Function (mathematics), 16. Peace & justice, Space (mathematics), Random walk, 01 natural sciences, Combinatorics, 010104 statistics & probability, Limit (mathematics), 0101 mathematics, Statistics, Probability and Uncertainty, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

Let ζ be a Markov chain on a finite state space D, f a function from D to ℝd, and Sn = ∑k=1nf(ζk). We prove an invariance theorem for S and derive an explicit expression of the limit covariance matrix. We give its exact value for p-reinforced random walks on ℤ2 with p = 1, 2, 3.

Published
1998
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11. Systemic Tail Risk Distribution

Author

null Alexis Bienvenüe and null Christian Y. Robert

Subjects
Statistics and Probability, Economics and Econometrics, Financial economics, 05 social sciences, Conditional probability distribution, 01 natural sciences, Stability (probability), 010104 statistics & probability, Expected shortfall, 0502 economics and business, Coherent risk measure, Economics, Systemic risk, Generalized extreme value distribution, Tail risk, 0101 mathematics, Statistics, Probability and Uncertainty, Social Sciences (miscellaneous), Value at risk, 050205 econometrics
Abstract

We introduce the systemic tail risk distribution of a financial market to characterize the asset return linkages during financial crisis. This distribution provides the probabilities that several assets of a market lose a large part of their nominal value given that the price of at least one of them collapses. It introduces a new way of assessing the stability of a financial market during potential systemic risk events. We propose a new type of multivariate extreme value distribution for high-dimensional vectors to model the extremal dependence between asset prices, and we use efficient likelihood inference methods to estimate the parameters of the systemic tail risk distribution. Our real data show that the empirical static systemic tail risk distribution is U-shaped, while the empirical conditional distribution is L-shaped.

Published
2016
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12. Iterative Adjustment of Survival Functions by Composed Probability Distortions

Author

Alexis Bienvenüe, Didier Rullière, Laboratoire de Sciences Actuarielle et Financière (SAF), Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon-Université de Lyon

Subjects
Hazard (logic), Economics and Econometrics, iterated compositions, [QFIN.RM]Quantitative Finance [q-fin]/Risk Management [q-fin.RM], 01 natural sciences, Stability (probability), 010104 statistics & probability, survival function transformation, Accounting, Impact modelling, 0502 economics and business, Econometrics, Economics, Applied mathematics, hyperbolic transform, 0101 mathematics, Event (probability theory), Parametric statistics, Estimation, 050208 finance, Risk measure, 05 social sciences, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, mortality, risk measure, Survival function, probability distortions, Business, Management and Accounting (miscellaneous), survival function transformation,hyperbolic transform,risk measure,probability distortions,mortality,iterated compositions, Finance
Abstract

International audience; We introduce a parametric class of composite probability distortions that can be combined to converge to a target survival function. These distortions respect analytic invertibility and stability, which are shown to be relevant in many actuarial fields. We study the asymptotic impact of such distortions on hazard rates. The paper provides an estimation methodology, including hints for initialisation. Some applications to survival data bring results for catastrophic event impact modelling. We also obtain accurate parametric representations of the mortality trend over years. Finally, we suggest a prospective mortality simulation model that comes naturally from the above analysis.

Published
2012
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13. On hyperbolic iterated distortions for the adjustment of survival functions

Author

Alexis Bienvenüe, Didier Rullière, Laboratoire de Sciences Actuarielle et Financière (SAF), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Perna, Cira, Sibillo, and Marilena

Subjects
Probability distortions, Hyperbolic secant distribution, iterated compositions, Risk measure, Mathematical analysis, Conversion function, Inverse, Inversion (meteorology), 02 engineering and technology, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, 01 natural sciences, risk measure, survival function transformation, 010104 statistics & probability, Survival function, Iterated function, 0202 electrical engineering, electronic engineering, information engineering, hyperbolic transform, Applied mathematics, 020201 artificial intelligence & image processing, 0101 mathematics, Mathematics
Abstract

This paper presents a class of distortions of survival functions. Studied distortions are built in order to respect several properties that seem to us useful in actuarial science. We focus here on some particular hyperbolic distortions, which preserve analytic invertibility of the distorted survival function, and for which inverse distortions belong to the same hyperbolic class. We propose some specific parameterizations of these distortions which give a straightforward inversion, and discuss the importance of such an inversion in insurance and finance. We prove the convergence of composed distortions to any target law, and give initial values and a particular methodology for the parameters estimation. Numerical figures illustrate the adaptation of these distortions to several actuarial fields.

Published
2012
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14. Sharp asymptotic results for simplified mutation-selection algorithms

Author

Alexis Bienvenüe, Jean Bérard, École nationale supérieure d'informatique et de mathématiques appliquées (ENSIMAG), Université Joseph Fourier - Grenoble 1 (UJF), Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon

Subjects
interacting particle systems, Statistics and Probability, Asymptotic analysis, Bessel process, Population, invariance principle, 01 natural sciences, Combinatorics, 010104 statistics & probability, 60F05, population dynamics, Quantitative Biology::Populations and Evolution, 0101 mathematics, education, ComputingMilieux_MISCELLANEOUS, Mathematics, education.field_of_study, [SHS.STAT]Humanities and Social Sciences/Methods and statistics, Invariance principle, large-deviations, 010102 general mathematics, random walks, 16. Peace & justice, Random walk, 92D15, Genetic algorithm, 60F17, Mutation (genetic algorithm), Asymptotology, Statistics, Probability and Uncertainty, 60F10
Abstract

We study the asymptotic behavior of a mutation--selection genetic algorithm on the integers with finite population of size $p\ge 1$. The mutation is defined by the steps of a simple random walk and the fitness function is linear. We prove that the normalized population satisfies an invariance principle, that a large-deviations principle holds and that the relative positions converge in law. After $n$ steps, the population is asymptotically around $\sqrt{n}$ times the position at time $1$ of a Bessel process of dimension $2p-1$.

Published
2003
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15. Niching in Monte Carlo Filtering Algorithms

Author

Olivier François, Eric Fontenas, Alexis Bienvenüe, Jean Bérard, Marc Joannides, Laboratoire de Modélisation et Calcul (LMC - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Statistiques et Analyse des Données (LABSAD), Université Pierre Mendès France - Grenoble 2 (UPMF), Laboratoire de Probabilités, Combinatoire et Statistique (LAPCS), Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon-Université de Lyon

Subjects
0209 industrial biotechnology, Mathematical optimization, Genetic Algorithm, [SHS.STAT]Humanities and Social Sciences/Methods and statistics, Computer science, Monte Carlo Algorithm, Rejection sampling, Monte Carlo method, Markov chain Monte Carlo, 02 engineering and technology, Genetic Algo, Hybrid Monte Carlo, symbols.namesake, 020901 industrial engineering & automation, Posterior Distribution, Interact Particle System, 0202 electrical engineering, electronic engineering, information engineering, symbols, 020201 artificial intelligence & image processing, Monte Carlo integration, Quasi-Monte Carlo method, Particle filter, Algorithm, Monte Carlo molecular modeling
Abstract

International audience; Nonlinear multimodal filtering problems are usually addressed via Monte Carlo algorithms. These algorithms involve sampling procedures that are similar to proportional selection in genetic algorithms, and that are prone to failure due to genetic drift. This work investigates the feasibility and the relevance of niching strategies in this context. Sharing methods are evaluated experimentally, and prove to be efficient in such issues.

Published
2002
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16. Convergence of a Genetic Algorithm with finite population

Author

Alexis Bienvenüe, Jean Bérard, Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon

Subjects
education.field_of_study, [SHS.STAT]Humanities and Social Sciences/Methods and statistics, Fitness function, Cultural algorithm, Population-based incremental learning, Population, 16. Peace & justice, Random walk, 01 natural sciences, 010104 statistics & probability, 0103 physical sciences, Convergence (routing), Genetic algorithm, Quantitative Biology::Populations and Evolution, Applied mathematics, Large deviations theory, 0101 mathematics, 010306 general physics, education, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

We study the asymptotic behaviour of a mutation-selection genetic algorithm on the integers with finite population, defined by a simple random walk and the fitness function f (x) = x. We prove the convergence in law of the normalized population and a large deviations principle.

Published
2000
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17. Global convergence for evolution strategies in spherical problems: some simple proofs and difficulties

Author

Olivier François, Alexis Bienvenüe, Laboratoire de Modélisation et Calcul (LMC - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - UMR 5525 (TIMC-IMAG), and VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)

Subjects
Mathematical optimization, Adaptive strategies, [SHS.STAT]Humanities and Social Sciences/Methods and statistics, General Computer Science, Markov chain, Markov chains, Computation, Chaotic, 0102 computer and information sciences, 02 engineering and technology, Mathematical proof, Global convergence, 01 natural sciences, Theoretical Computer Science, Evolution strategies, 010201 computation theory & mathematics, Simple (abstract algebra), Convergence (routing), 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Mathematics, Computer Science(all)
Abstract

International audience; This paper presents simple proofs for the global convergence of evolution strategies in spherical problems. We investigate convergence properties for both adaptive and self-adaptive strategies. Regarding adaptive strategies, the convergence rates are computed explicitly and compared with the results obtained in the so-called “rate-of-progress” theory. Regarding self-adaptive strategies, the computation is conditional to the knowledge of a specific induced Markov chain. An explicit example of chaotic behavior illustrates the complexity in dealing with such chains. In addition to these proofs, this work outlines a number of difficulties in dealing with evolution strategies.

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