### Groupe de Travail sur la Longévité

 Laboratoire de Probabilités et Modèles AléatoiresLe Groupe de Travail sur la Longévité a lieu le vendredi de 13h45 à 15h à l'adresse suivante :Université Pierre et Marie Curie - 4 Place Jussieu - 75005 Paris (Métro Jussieu)Couloir 16-26, Salle 113 (1er étage)Organisation : Nicole El Karoui, Sarah Kaakai, Caroline Hillairet, Olivier Lopez.Le site du GT Longévité a changé! Les informations concernant les prochaines séances seront publiées à l'adresse suivante:Prochaine séance   Vendredi 22 Septembre 2017 à 13h45 Séance commune Valeurs extrêmes et LongévitéSéances précédentes 9 juin 2017:>Pierrick Piette (ISFA, Univ. Lyon 1 )Mortality Rates Forecasting with High-Dimensional Vector-AutoregressionsAbstract: The mortality rates forecasting problem involves the analysis of high-dimensional time series, especially in multi-populations modelling. Most of usual mortality models propose to decompose the mortality rates into several latent factors to reduce this complexity. These approaches, in particular those used cohort factors, have a good fit, but they are less reliable for forecasting purpose. One of the major challenges is to determine the spatial-temporal dependence structure between mortality rates given a relative moderate sample size. This paper proposes a large vector autoregressive (VAR) model fitted on the differences in the log-mortality rates, ensuring that the existence of long-run relationships between the mortality rates improvements. Our contribution is threefold. First, sparsity when fitting the model is ensured by using high-dimensional variables selection techniques without imposing arbitrary constraints on the dependence structure. The main interest is that the structure of the model is directly driven by the data, in contrast to the main mortality forecasting models. Additionally, our estimation allows a one-step process, as we do not need to estimate hyper-parameters. The variance-covariance matrix of residuals is then estimated through a parametric form. Secondly, our approach can be used to detect no intuitive age dependence in the data, beyond the cohort effect which is captured by our model. Third, our approach is natural to model the several populations in long run perspectives. Finally, in an out-of-sample forecasting study for mortality rates, we obtain a significant performance increasing when compared to classical mortality models using the French, US and UK data. We also show that our results enlighten the so-called cohort effect for these populations.12 mai  2017:>Sophie Hautphenne (Univ. of Melbourne and EPFL, Lausanne )The Markovian binary tree applied to demography Abstract: We apply matrix analytic methods and branching processes theory to a comparison of female populations in different countries. We show how the same mathematical model allows us to determine characteristics about individual women, such as the distribution of her lifetime, the time until her first and her last daughter, and the number of daughters, as well as to analyze properties of the whole female family generated by a first woman, such as the extinction probability of the family, the distributions of the time until extinction, of the family size at any given time and of the total progeny. In a second part, we consider a class of continuous-time branching processes called Markovian binary trees, in which the individuals lifetime and reproduction epochs are modeled using a transient Markovian arrival process (TMAP). Motivated by datasets on human populations and on the endangered Chatham Island black robin bird species, we develop methods for estimating the parameters of the TMAP, using age-specific global population data and individual demographic data, respectively. Depending on the degree of detail of the available information, a weighted non-linear regression method or a maximum likelihood method is applied.  We discuss the optimal choice of the number of phases in the TMAP, and we provide confidence intervals for the model outputs. We gain insights about the conservation of the black robin population through this method of analysis. References: -  Hautphenne, S., Massaro, M., & Turner, K. (2017). Fitting Markovian binary trees using global and individual demographic data. arXiv preprint arXiv:1702.04281.-  Hautphenne, S., & Latouche, G. (2012). The Markovian binary tree applied to demography. Journal of mathematical biology, 64(7), 1109-113528 avril 2017:> Marc Hoffmann (CEREMADE, Paris)Nonparametric estimation of an inhomogeneous age-dependent model in a large population limit  Abstract: Motivated by improving mortality tables from human demography databases, we investigate inference of an age-evolving density of a population alimented by time inhomogeneous mortality and fertility. We understand our approach as a first rigorous step in order to improve mortality (or fertility) rate estimation following Boumezoued 2016. Asymptotics are taken as the size of the population grows within a limited time horizon: the observation gets closer to the solution of a PDE (a inhomogeneous version of the Von Foerster Mc Kendrick equation) and the difficulty lies in controlling simultaneously the approximation to the limiting PDE in a suitable sense together with an appropriate parametrisation of the anisotropic solution. In this setting, we prove new concentration inequalities that enable us to implement the Goldenshluger-Lepski algorithm and derive oracle inequalities. Minimax lower bounds are investigated and links to inverse problems for the fertility rate estimation are identified. This is a joint work with A. Boumezoued and P. Jeunesse. 08 avril 2017:> Kaouther Hadji (LPMA, Paris VI) Simulation of population heterogeneityAbstract: In this talk, I will present simulation techniques for the microscopic  evolution of individual life courses based on Thinning procedure. The  efficiency of the simulation model is illustrated using a simplified  example that aims to reproduce demographic events such as Cohort  effect considered by Alexander Boumezoued (2006) and inspired by the work of Willets (2004) on the Golden Cohort in UK. Baby boom phenomena  can be also of great interest to illustrate the potential impact of  heterogeneous birth rates on aggregate mortality.Firstly, we will show how we can simulate individual life courses  evolution in a large homogeneous population (which can be simulated by  considering the data on French population available in the database HMD) by the visualization of age pyramids that can be generated for  100 years in few seconds (implemented by Vincent Lemaire). Then, we  will divide the initial population into two sub-populations that  behave differently in terms of birth and death (for instance, rich and poor sub-populations). The impact of the evolution of such heterogeneous population on aggregated mortality indicators will be  explained through the computation of life expectancy, force of mortality, etc.24 février 2017:> Gilles Gaba (ISFA, Lyon)Introduction aux systèmes anthropologiques, et à leurs potentielles utilisations en cliométrie démographique et économique.Abstract: Les systèmes anthropologiques sont-ils utiles à la compréhension des phénomènes économiques et démographiques ? Depuis l’après-guerre, l’anthropologie sociale fait l’objet d’intenses recherches pour des usages divers comme en diplomatie, en management d’entreprises multinationales ou en science politique. Dans un premier temps, nous présenterons les principaux systèmes anthropologiques et leurs dimensions,puis dans une seconde phase nous évoquerons quelques utilisations potentielles de ces systèmes en cliométrie démographique et économique.3 février 2017:>  Thibault Allart (LSTA, Paris VI)Analyse de données longitudinales : application aux jeux vidéoAbstract: Historiquement issues des études cliniques où elles restaient cantonnées à des échantillons de petite taille, les données longitudinales sont aujourd'hui de plus en plus nombreuses. Des traces de navigation internet des utilisateurs d'e-commerce, aux objets connectés, en passant par nos parcours de santé enregistrés sur nos cartes vitales; leur particularité est qu'elles sont désormais de grande taille. Ces grands échantillons permettent d'envisager des modèles plus complexes, tels que des coefficients variationnels en temps. En s'appuyant sur la théorie des processus de comptage, nous présenterons un modèle de survie adapté à ces données. Nous montrerons que, contrairement au modèle de Cox, l'estimation de ce modèle peut être effectuée "en ligne", offrant dès lors la possibilité d'utiliser des algorithmes de type descente de gradient stochastique, plus performants sur ces échantillons de grande taille. Nous illustrerons cette approche sur des simulations en nous comparant aux méthodes existantes. L'ensemble de l'exposé se fera sur le thème des jeux vidéo et nous présenterons une mise en application industrielle visant à améliorer le design des jeux vidéo.20 janvier 2017:>  Martino Grasseli (ESILV, Paris) Insurance Demographic Risk Sharing in Defined Contribution Pension Systems Abstract: In this talk we formulate and solve the optimal design problem of a defined contribution public pension fund, in a highly stylized but still rather general non-stationary framework. We adopt the viewpoint of a benevolent socialplanner who aims at treating in a fair manner the successiveoverlapping generations participating to such a long-term mandatory system. Using the approach of El Karoui and Jeanblanc (1998) for the optimal consumption and portfolio choice problem with random income in a complete market, we exhibit a solution to our intertemporal stochastic control problem where each generation receives a fair (lumpsum) retirement benefit: it is proportional to the contributions she has paid during her active worklife and follows a fixed common rule (although her pension value itself may depend on variables only observable at her retirement time. We next relax the assumption that the collective pension system is mandatory and investigate the performance of individual investment plans in the market. Comparing the outcomes of both alternatives, we derive a condition under which the collective fund can be expected to overperform the individual plan. In the special case of a stationary economy, such a possibility has been pointed out by Gollier(2008). In fact this effect results from the possibility for the collective fund to borrow today against contributions of future generations, which allows to implement riskier strategies and may improve its performance.(link to article)06 janvier 2017:>  Quentin Guibert (ISFA, Lyon) Non-Parametric Inference of Transition Probabilities Based on Aalen-Johansen Integral Estimators for Acyclic Multi-State Models: Application to LTC Insurance Abstract: Studying Long Term Care (LTC) insurance requires modelling the lifetime of individuals in presence of both terminal and non-terminal events which are concurrent. Although a non-homogeneous semi-Markov multi-state model is probably the best candidate for this purpose, most of the current researches assume, maybe abusively, that the Markov assumption is satisfied when fitting the model. In this context, using the Aalen-Johansen estimators for transition probabilities can induce bias, which can be important when the Markov assumption is strongly unstated. Based on some recent studies developing non-Markov estimators in the illness-death model that we can easily extend to a more general acyclic multi-state model, we exhibit three non-parametric estimators of transition probabilities of paying cash-flows, which are of interest when pricing or reserving LTC guarantees in discrete time. As our method directly estimates these quantities instead of transition intensities, it is not needed to develop intermediary numerical techniques to resolve a set of Kolmogorov differential equations. Our estimators satisfy some asymptotic results under non-dependent random right-censorship, that we obtain by re-setting the system with two competing risk blocks. Inclusion of left-truncation is also considered. We conduct simulations to compare the performance of our transition probabilities estimators without the Markov assumption. Finally, we propose a numerical application with LTC insurance data, which is traditionally analyzed with a semi-Markov model.  02 décembre 2016 :> Annamaria Olivieri High Age Mortality, Frailty and Risk Classification for a Life Annuity Portfolio (slide)Abstract : The age-pattern of mortality rates at very old ages shows, in many populations, a slowed increase. Causes of this deceleration have been explained in different ways. An analytical justification is, in particular, provided by the (likely) heterogeneity of the population with respect to mortality, which can be formally described with a frailty model. The presence of mortality heterogeneity can have an impact on the risk profile of a life annuity portfolio (or a pension fund). While the adoption of frailty models for the representation of mortality is well-known, their application for risk management purposes is not common. In this research we focus on a potential application of the frailty model, which can be helpful to design a rating structure for life annuities. Voluntary life annuities are mainly underwritten by healthy people. In order to expand their business, in recent years some insurers have started offering special annuity rates to those whose health conditions are critical. As a result of such a strategy, risk classes can be identified within the portfolio, showing different levels of mortality. In general, the level of mortality in life annuity portfolios is lower than for the general population. Mortality rates for annuitants are usually obtained by applying reduction coefficients to the population mortality rates. According to common actuarial practice, such coefficients are chosen empirically, calibrated on the average ratio (possiblymeasured for age-groups) between the annuitants’ and the population mortality rates; conversely, a model formally justifying such a difference is not adopted. Within a frailty model, lower mortality rates can be justified by lower frailty levels. Thus, we identify risk groups (or classes) within the population by assigning specific ranges of values to the frailty within each group. Conditional probability distributions for the frailty are obtained for each risk class, which allow us to describe the different levels of mortality of the various groups. This way we design a rating system, as different values for the annuity rate derive from the different assumptions about the frailty level of the specific risk class. We also investigate the following issue. When dealing with several risk classes, the insurer may increase its portfolio size, but also the heterogeneity of the portfolio. While a larger size implies an improved pooling effect, a higher risk profile follows from the increased heterogeneity. We investigate the result of this trade-off. The risk profile of the portfolio is examined in terms of the dispersion of the probability distribution of the present value of future benefits. Portfolios without and with risk classification are compared, so to measure the trade-off between size and heterogeneity.Keywords: Voluntary annuities, Underwritten annuities, Standard risk, Preferred risk, Issue-select mortality rates.References:[1] A. Olivieri and E. Pitacco (2016). Frailty and risk classification for a life annuity portfolio. Risks, vol. 4(4): 39.[2] E. Pitacco (2016). High age mortality and frailty. Some remarks and hints for actuarial modelling. Working Paper 2016/19, ARC Centre of Excellence in Population Ageing Research. Available at: http://www.cepar.edu.au/media/167251/19-high-age-mortality-and-frailty-some-remarks-and-hints-for-actuarial-modeling.pdf18 novembre 2016 :>  Sarah Kaakai ( LPMA, Paris VI)Understanding the aggregated mortality via stochastic modeling of heterogeneous population dynamicsAbstract : The study of human longevity have brought to light the key role of certain intrinsic characteristics such as gender. For instance, women lives in averaged six years longer that men. On the other hand, it has been shown that so-called social characteristics (education, place ofliving...) have equally played a determining role in the evolution of longevity. In addition, the distribution of these social characteristics is all but stationary, and can change a fast pace.Often, the only observable data are aggregated data. However, the complexity of the evolution of heterogeneity in the population makes it difficult to apprehend its evolution directly on an aggregated level. An more detailed population model is thus useful in order to report for the social composition of the population and its changes, and to explore its influence on aggregated longevity.In the wake of recent advances in population dynamics, we model the evolution of an heterogeneous population as a Birth-Death-Swap system with stochastic intensities. After an introduction on the modelling of population dynamics by thinning of Poisson processes and its link to simulations, we will develop a new construction of the population as a sequence of Swap systems interacting with the aggregated population.This representation is more adequate when characteristics changes occur at a fast timescale in comparison with the demographic timescale, and will be used to show that the separation of timescale allows to make some averaging approximations for the aggregated process.7 octobre 2016 :>  Sabine Zinn ( Leibniz Institute for Educational Trajectories, Bamberg)Simulating Synthetic Life Courses of Individuals and Couples, and Mate MatchingAbstract : In this talk, I present a simulation model and related simulation techniques facilitating the description of life courses of individuals and couples and conducting mate matching.To define individual and couple behaviour a continuous-time multi-state model is used. For mate matching agent-based modelling is applied. That way, interdependencies between individuals and between the life-courses of spouses can be accounted for. The capability of the simulation model is illustrated using a simplified example that aims at forecasting a hypothesized population based on the population of the Netherlands with a focus on partnership stability and smoking behavior.23 septembre:>  Jennifer Alonso García, (CEPAR, Sydney) Economic and demographic risks for pay-as-you-go pension schemes: Defined Benefit versus Defined Contribution27-28 juin 2016 : >   First Lyon-Columbia research workshop on Actuarial Science, Quantitative Risk Management and Data Science for insurance and finance, ISFA, Lyon. Program and registration here.Jeudi 16 juin 2016 :>  17h30 - 18h30, Séance commune GT Longévité/GT Finance  : Saïd Hamadene, Univ. du Maine.Weak formulation of mean-field control problemsRésumé : We deal with the weak formulation of the mean-field control problem and the mean-field zero-sum differetial game as well. We show  existence of an optimal control and a saddle-point for respectively  the control problem and zero-sum differential game associated with  payoff functionals of mean-field type, under dynamics driven by weak  solutions of stochastic differential equations of mean-field type.29 janvier 2016 :>  Yann Le Cunff,  Université Rennes 1. Ageing : Between Evolution and DemographyRésumé:  Aging is a complex, multiscale issue, at the interface between evolution and demography. The disposable soma theory, an evolutionary theory of aging, proposes that trade-offs between maintenance and reproduction drive aging. Despite its success at describing similarities in aging at the individual level, the disposable soma theory does not provide insights about mortality patterns observed across species. By contrast, biodemographic studies of aging show that population heterogeneity explains these mortality patterns. Yet, they do not address whether population heterogeneity derives from evolutionary processes.In this presentation we will intend to bridge this gap between evolutionary and demographic approaches of ageing. To do so, we will develop minimal mathematical models, in which population heterogeneity evolves over generations. Then, we will compare the resulting simulated mortality patterns with experimental and empirical data, in order to shed light on key processes involved in the evolution of ageing. 7 décembre 2015 :>  Conference day of the joint project LPMA, Univ Paris 6 - DSA, Univ Lausanne on Causes of Death Mortality and Population Dynamics.Financed by PHC Germaine de Staël.Abstract :The "Germaine de Staël" program "Modélisation des causes de décès dans la dynamique des populations" (Gds 2014-14) is a research project between the DSA (Département de Sciences Actuarielles), University of Lausanne, and the LPMA (Laboratoire de Probabilités et Modèles Aléatoires), University Paris 6, comprising Séverine Arnold, Alexandre Boumezoued, Nicole El Karoui, Sarah Kaakai and Héloïse Labit Hardy.This project focuses on cause-of-death mortality changes and their impacts on the whole population evolution. To this aim, this project combines two fields: the modeling of cause-of-death mortality and population dynamics techniques. Whereas previous studies on causes of death focus on mortality indicators, our aim is to get additional insights by including birth patterns. In the first instance, our numerical results based on French data show that populations with identical life expectancies can present important differences in their age pyramid resulting from different cause-specific mortality reductions. As a second step, we study how initial age pyramid and/or birth rates patterns in a heterogeneous population could compensate a potential cause specific mortality reduction. We apply this study with English data on cause-of-death and characteristic-specific mortality.Program 20 novembre 2015 :> 13h45-15h : Agathe Guilloux (LSTA, Univ Paris 6)Apprentissage statistique pour données observationnelles longitudinales (longitudinal observational data)Résumé: A partir de trois exemples de données (issues d’un système de santé, d’une mutuelle santé et marketing), nous montrons les nouveaux challenges statistiques que présentent ces données, et les questions associées. Des modèles de régression dynamique en grande dimension et pour temps d'occurrence seront introduits. Je présenterai ensuite les procédures d'estimation dans ces modèles, quelques les résultats obtenus, et les aspects algorithmiques (calcul des estimateurs). Enfin je présenterai des extensions possibles des modèles présentés. 16 octobre 2015 :> 13h45-15h : Alexandre Boumezoued ( Milliman R&D, LPMA)Measuring mortality heterogeneity with multi-state models and interval-censored dataRésumé: Joint work with Nicole El Karoui and Stéphane Loisel.In this work, our aim is to measure mortality rates which are specific to individual observable factors when these can change during life. The study is based on longitudinal data recording marital status and socio-professional features at census times, therefore the observation scheme is interval-censored since individual characteristics are only observed at isolated dates and transition times remain unknown. To this aim, we develop a parametric maximum likelihood estimation procedure for multi-state models that takes into account both interval-censoring and reversible transitions. This method, inspired by recent ad- vances in the statistical literature, allows us to capture characteristic-specific mortality rates, in particular to recover the mortality compensation law at high ages, but also to capture the age pattern of characteristics changes. The dynamics of several population compositions is addressed, and allows us to give explanations on the pattern of aggregate mortality, as well as on the impact on typical life insurance products. Particular attention is devoted to characteristics changes and parameter uncertainty that are both crucial to take into account. 24 septembre 2015:> 16h30 - 17h45 :  Adam Shao ( ARC Center of Excellence in Population Ageing Research. UNSW Business School, Sydney) Managing Retirement Risks with Reverse Mortgage Loans and Long-Term Care InsuranceRésumé: Joint work with Hua Cheny and Michael Sherris.This paper investigates a retiree's optimal portfolio choice with respect to consumption, reverse mortgage loans, and private long-term care insurance. We use a discrete time life-cycle model that takes into account mortality risk, health shocks and houseprice risk. The results of this paper have implications as to how individuals can use reverse mortgage loans and private long-term care insurance to better manage retirement risks. In particular, we quantify the extent to which the demand for private long-term care insurance is weakened by home equity. The interacting effects between reverse mortgage and private long-term care insurance are investigated. We show that 65-year-old females would have 5.7% welfare gain if they have access to reverse mortgage only. The welfare gain would be 7.1% when private long-term care insurance is added to the menu. Our analysis provides insights into the design of linking reverse mortgage loans and long-term care insurance.26 juin 2015 :> 13h45 - 15h00 :  Jessica Tressou Cosmao (INRA UMR MIA Paris)Extreme values statistics for Markov chains via the (pseudo-) regenerative methodRésumé: http://link.springer.com/article/10.1007%2Fs10687-009-0081-yJoint work with Patrice Bertail (Paris X) and Stéphan Clémençon (TelecomParisTech)22 mai 2015 :> 13h45 - 15h00 :  Héloise Larbit Hardy (Université de Lausanne)Cause-of-Death Mortality: What Can Be Learned From Population Dynamics?Résumé: This paper analyzes cause-of-death mortality changes and its impacts on the whole population evolution. The study combines cause-of-death analysis and population dynamics techniques. Our aim is to measure the impact of cause-of-death reduction on the whole population age structure. Whereas previous studies on causes of death focused on mortality indicators such as survival curves or life expectancy, our approach provides additional information by including birth patterns. As an important conclusion, our numerical results based on French data show that populations with identical life expectancies can present important differences in their age pyramid structure resulting from different cause-specific mortality reductions.Joint work with Séverine Arnold , Alexandre Boumezoued and Nicole El Karoui.10 avril 2015 :> 13h45 - 15h00 : Edouard Debonneuil (Celtipharm)Questionning longevity trends and cohort effectsRésumé: A set of tools such as Lee Carter-like models and heat plots to visualize cohort effects have been established to model longevity. Visualizing and modeling longevity with different angles and for general populations suggests some misconceptions and adds some clarity, but the future remains of course unknown. 27 mars 2015 :> 13h45 - 15h00 :  Xavier Milhaud (ENSAE)Consistency of tree-based estimators in censored regression with applications in insurance  Résumé: The use of regression trees as a tool for high-dimensional classification and regression problems has boomed since the publication of [Breiman,1984]. Initially designed to estimate nonparametrically the conditional mean of a response given some covariates, this popular technique is here adapted to deal with survival data. We derive key nonasymptotic results and almost sure convergence rates for tree-based estimators provided by the growing procedure, as well as convergence properties of the associated selection process. Our theoretical results are confirmed thanks to a simulation study, and two applications on insurance datasets enable to illustrate the utility of such a method in a real-life context.30 Janvier 2015 : > 13h45 - 15h00 : Guillaume Biessy (LPMA -SCOR)Construction d'un modèle multi-états semi-markovien pour le processus de dépendance chez les personnes âgéesRésumé: La tarification des produits d'assurance dépendance se base aujourd'hui sur des modèles simples, où la dépendance est considérée comme un état unique et homogène. En raison du vieillissement de la population et des progrès rapides de la médecine, il est primordial d'acquérir une vision plus claire de ce risque, aujourd'hui très peu maîtrisé. Nous pensons que cet objectif peut être atteint en prenant en compte plusieurs niveaux de dépendance. Un processus multi-états est dit semi-markovien lorsque les probabilités de transition du processus dépendent à la fois de l'état actuel et du temps passé dans cet état. De tels processus s'avèrent plus flexibles que les processus markoviens simples, et ont fait l'objet de nombreuses publications dans le domaine de l'épidémiologie. Cependant, leur application à l'assurance dépendance est restée principalement théorique, en raison notamment du manque de données accessibles aux assureurs.Nous allons présenter la démarche de construction d'un modèle semi-markovien considérant deux niveaux de dépendance. Ce travail s'appuie sur des données recueillies dans le cadre de l'AllocationPersonnalisée d'Autonomie (APA). Tout d'abord, nous introduisons les paramètres intervenant dans la modélisation des transitions entre les états. Nous procédons ensuite à l'estimation de ces paramètres par la méthode du maximum de vraisemblance, en tenant compte des spécificités liées aux données. Enfin, nous proposons une application du modèle à la tarification d'un produit d'assurance dépendance fictif, à l'aide d'une méthode de type Monte Carlo.16 Janvier 2015 : Reprise du GT Longévité> 13h45 - 15h00 : Hippolyte d'Albis (Ecole d'Economie de Paris - Université Paris 1)Immigration Policy and Macroeconomic Performance in FranceRésumé: This paper quantitatively assesses the interaction between permanent immigration into France and France’s macroeconomic performance as seen through its GDP per capita and its unemployment rate. It takes advantage of a new database where immigration is measured by the flow of newly-issued long-term residence permits, categorized by both the nationality of the immigrant and the reason of permit issuance. Using a VAR model estimation of monthly data over the period 1994-2008, we find that immigration flow significantly responds to France’s macroeconomic performance: positively to the country’s GDP per capita and negatively to its unemployment rate. At the same time, we find that immigration itself increases France’s GDP per capita, particularly in the case of family immigration. This family immigration also reduces the country’s unemployment rate, especially when the families come from developing countries. Joint work with Ekrame Boubtane and Dramane Coulibaly.13 Juin 2014 : Séance commune GT Longévité - GT Théorie des valeurs extrêmes> 13h30 - 14h30 : Michel Broniatowski (LSTA) Sums and extremes> 14h30 - 15h30 : Philippe Soulier (MODAL'X)Le diamètre d'un nuage de points: comportement asymptotique dans quelques cas simples.Résumé: Jammalamadaka and Janson (2012, arXiv:1211.0822) ont récemment étudié le comportement asymptotique du diamètre d'un nuage de points sphériques (i.e. l'angle est indépendant du rayon et la loi de l'angle uniforme), lorsque le rayon est dans le domaine d'attraction de la loi de Gumbel. Comme on s'y attend, le diamètre se comporte comme à peu près deux fois le maximum des normes, et converge vers la loi de Gumbel, cependant à un terme correctif tendant vers l'infini près. Dans le cas non sphérique (l'angle n'est pas indépendant du rayon), n'importe quelle situation est possible. Nous étudions les lois elliptiques qui contiennent notamment les lois Gaussiennes non isotropes qui ne sont pas couvertes par le résultat de Jammalamadaka et Janson, et quelques généralisations. De même que pour le problème plus ancien des loi limites conditionnellement à une composante extrême, la géométrie des lignes ou surfaces de niveaux de la densité du vecteur est déterminante.Travail joint avec Yann Deminchel et Ana-Karina Fermin.> 15h30 - 16h30 : Maud Thomas (LPMA) Prédire des épidémies de grippe exceptionnelles : une introduction à la théorie des valeurs extrêmes Résumé: La théorie des valeurs extrêmes a été appliquée dans beaucoup de do- maines tels que l’environnement, la génétique ou encore la finance pour pré- dire des événements extrêmes. Une question centrale pour la planification des ressources en santé publique serait de prévoir la conséquence de la mortalité due à des épidémies de grippe particulièrement meurtrières. Le but de cet exposé est d’introduire la théorie des valeurs extrêmes à travers cet exemple en montrant comment mettre en oeuvre la méthode des maxima par blocs et à quelles questions nous pouvons tenter de répondre. 16 mai 2014 - William Kengne (THEMA, Univ. Cergy-Pontoise)    Testing for structural change in time series of counts (Joint work with P. Doukhan)Abstract: In this talk we consider together the inference questions and the change-point problem in Poisson autoregressions model. The conditional mean (or intensity) of the process is involved as a non-linear function of it past values and the past observations. Under Lipschitz-type conditions, it is shown that the conditional mean can be written as a function of lagged observations. In the latter model, assume that the link function depends on an unknown parameter $\theta_0$. The consistency and the asymptotic normality of the maximum likelihood estimator of the parameter are proved. These results are used to study change-point problem in the parameter $\theta_0$. We propose two tests based on the likelihood of the observations. The consistency of these tests under the null hypothesis (of no change) as well as under the alternative are proved. Some simulation results  and real data application are reported.4 Avril 2014 - Laurent Devineau (Milliman)          Simulations dans les simulations et utilisation de la probabilité risque-neutre en assuranceRésumé : L’objectif de cet exposé est de présenter les différentes problématiques simulatoires auxquelles sont soumis les opérationnels de l’assurance dans le dispositif Solvabilité II. Dans une première partie nous nous intéresserons à la problématique du calcul du capital économique réglementaire. Nous développerons les notions qui sous-tendent ce calcul avant de proposer des exemples de mise en œuvre pratique. Puis nous nous attacherons à expliciter les difficultés introduites par la simulation des différents scénarios économiques utilisés dans ce cadre. Dans une seconde partie nous nous intéresserons aux problématiques de calcul numérique liées aux approches présentées. Nous baserons notre intervention sur les méthodes permettant d’optimiser le temps et la complexité de calcul.14 Mars 2014 - Olivier Lopez (CREST, ENSAE & LSTA, Univ. Paris 6)          Méthodes non paramétriques pour l'analyse conjointe de durées de vie dans un coupleRésumé : Dans cet exposé, on considère le problème de l'étude de la durée de vie de deux membres d'un même couple. On définit un nouvel               estimateur non paramétrique de la distribution jointe de ces deux variables, en tenant compte des phénomènes de censure et de troncature. La construction de cet estimateur est basée sur la version empirique d'une équation aux dérivées partielles qui caractérise le modèle de censure/troncature. On s'intéressera à l'utilisation de ce nouvel estimateur pour construire des procédures de tests d'adéquation à des modèles de copules, et on discutera de son adaptation à la prise en compte d'une évolution temporelle dans la structure de dépendance.14 Février 2014 - Grégory Nuel (LPMA, Université Paris 6)Cancer Risk Assessment from Family History: the DECURION projectAbstract: In this talk we present a survival model (with genetic exposure and familial frailty) which is used to predict the risk of cancer from family history (and possible complementary genetic investigations). We briefly explain how it is possible to perform computations on this model (ex: likelihood with incomplete data, posterior distribution of variables of interest, etc.) using belief propagation in Bayesian networks. We introduce the problem of estimation under ascertainment and show some simulation to illustrate the problem.31 Janvier 2014 - Fabienne Comte (MAP5, Université Paris Descartes)Modèles de survie en présence de censure : estimation non paramétrique du risque instantané6 Décembre 2013 - Svetlana Gribkova (LSTA, Univ. Paris 6)        Méthodes non-paramétriques pour l'étude de dépendance de durées de vie22 Novembre 2013- Yang Lu (CREST) Love and Death: a Freund Model with Frailty15 Novembre 2013- Nicole El Karoui (LPMA, Univ. Paris 6)        Fast change detection on proportional two-populations hazard rates 18 Juin 2013 - Julien Vedani (Milliman & ISFA, Univ. Lyon 1)  Simulations dans les simulations pour le calcul du capital économique en assurance-vie11 Juin 2013 - Vincent Lemaire (LPMA, Univ. Paris 6) Simulation d'un modèle microscopique de dynamique des populations28 mai 2013 - Séverine Gaille (UNIL, HEC Lausanne)         Mortalité : qu'en est-il des causes de décès ?19 mars 2013 - Harry Bensusan (Crédit Agricole CIB) Une méthode de transfert du risque de taux d'intérêt associé à la longévité 05 mars 2013 - Nicole El Karoui (LPMA, Univ. Paris 6) Modèle de dynamique des populations 2 : modèle d'évolution avec prise en compte de l'âge et de caractéristiques individuellesNicole El Karoui (LPMA, Univ. Paris 6) - 26 févrierModèle de dynamique des populations 1 : introduction aux processus ponctuels et aux modèles de populationsAlexandre Boumezoued (LPMA, Univ. Paris 6) - 19 févrierModèles de mortalité 2 : hétérogénéité et prise en compte de caractéristiques individuellesAlexandre Boumezoued (LPMA, Univ. Paris 6) - 12 février        Modèles de mortalité 1 : données, estimation et projectionYves Lehmann (UBS) - 05 février  Variable Annuities : erreurs de modèle, arbitrages réglementaires et risques systémiquesContact : sarah.kaakai " a t " [upmc] "dot" f