CHARPENTIER Arthur

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The Pareto model is very popular in risk management, since simple analytical formulas can be derived for financial downside risk measures (value-at-risk, expected shortfall) or reinsurance premiums and related quantities (large claim index, return period). Nevertheless, in practice, distributions are (strictly) Pareto only in the tails, above (possible very) large threshold. Therefore, it could be interesting to take into account second-order behavior to provide a better fit. In this article, we present how to go from a strict Pareto model to Pareto-type distributions. We discuss inference, derive formulas for various measures and indices, and finally provide applications on insurance losses and financial risks.

Sites that offer their users to reconstruct their family tree online are flourishing on the Internet. This article analyzes the work of collection and data entry carried out by these users and how it could be used in historical demography, in order to complete the knowledge of past generations. To do so, the results obtained from the Geneanet database are compared with those known from the literature, and concern the records of 2,457,450 French individuals or individuals of French origin who lived in the 19th century. A significant bias in the sex ratio (under-representation of women) is thus highlighted. Fertility is also strongly underestimated. As for mortality (in comparison with historical values), these data underestimate male mortality up to about 40 years of age and female mortality up to 25 years of age, and then overestimate it. Finally, the wealth of spatial characteristics contained in the family trees is also exploited to produce new data on internal migration in the nineteenth century.

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We consider here an extended SIR model, including several features of the recent COVID-19 outbreak: in particular the infected and recovered individuals can either be detected (+) or undetected (-) and we also integrate an intensive care unit capacity. Our model enables a tractable quantitative analysis of the optimal policy for the control of the epidemic dynamics using both lockdown and detection intervention levers. With parametric specification based on literature on COVID-19, we investigate sensitivity of various quantities on optimal strategies, taking into account the subtle tradeoff between the sanitary and the economic cost of the pandemic, together with the limited capacity level of ICU. We identify the optimal lockdown policy as an intervention structured in 4 successive phases: First a quick and strong lockdown intervention to stop the exponential growth of the contagion. second a short transition phase to reduce the prevalence of the virus. third a long period with full ICU capacity and stable virus prevalence. finally a return to normal social interactions with disappearance of the virus. We also provide optimal intervention measures with increasing ICU capacity, as well as optimization over the effort on detection of infectious and immune individuals.

The continuous increase in computer performance over the past decades has allowed for the widespread application of statistical learning theory in many fields. In particular, actuaries, historical experts in statistics, are increasingly turning to these innovative algorithms for the assessment of the risks they face. Thus, in this thesis, we examine how the integration of methodologies from statistical learning can contribute to the development of actuarial sciences and risk management through the study of three independent problems, presented in a general introduction. The first two chapters propose new mortality projection models in the context of the evaluation of longevity risk carried by insurance companies or pension funds. Chapter 1 focuses on the case where a single population is studied, while Chapter 2 extends the analysis to multi-populations. In both situations, the problem of high dimensionality appears central and we address it using a penalized vector autoregression (VAR). This model is applied directly on the mortality improvement rates in the first chapter, and on the time series resulting from the estimation of a Lee-Carter model for the second. The elastic-net penalty allows us to keep the great freedom of the space-time dependence structure offered by the VAR while remaining parsimonious in the number of parameters, and thus avoid overlearning. In Chapter 3 we analyze the surrender risk of life insurance contracts using supervised classification algorithms. Among others, we apply the wide margin separator (SVM) and the extreme gradient boosting (XGBoost). In order to compare the performances of the different classifiers, we adopt an economic vision from the marketing literature based on the potential profits of a retention campaign. We insist on the importance of the loss function retained in the statistical learning algorithms according to the objective sought: the use of a loss function in connection with the performance measure brings a significant improvement in the application of the XGBoost in our study. Finally, in the context of financial risk management, we study the dynamics of agricultural prices during particular trading sessions where government reports, containing valuable information for agents, are published. We examine the potential of open access data, in particular satellite images of vegetation index made available by NASA, for predicting market reactions. We then propose avenues of improvement to consider for practical implementation of this data enrichment methodology in risk management.

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Technology companies and the insurance world would have everything to be opposed. Agility, speed, obsession with the future for some, conservatism, reflexivity, fascination with past data for others. And yet, both are observing each other, and are starting to form partnerships, understanding that data is their core business.

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The digital age allows data collection to be done on a large scale and at low cost. This is the case of genealogy trees, which flourish on numerous digital platforms thanks to the collaboration of a mass of individuals wishing to trace their origins and share them with other users. The family trees constituted in this way contain information on the links between individuals and their ancestors, which can be used in historical demography, and more particularly to study migration phenomena. The case of 19th century France is taken as an example, using data from the family trees of 238,009 users of the Geneanet website, or 2.

In the summer of 2013, the term "Big Data" made its appearance and aroused strong interest among companies. This thesis studies the contribution of these methods to actuarial sciences. It addresses both theoretical and practical issues on high-potential topics such as textit{Optical Character Recognition} (OCR), text analysis, data anonymization or model interpretability. Starting with the application of machine learning methods in the calculation of economic capital, we then try to better illustrate the frontality that can exist between machine learning and statistics. Putting forward some advantages and different techniques, we then study the application of deep neural networks in the optical analysis of documents and text, once extracted. The use of complex methods and the implementation of the General Data Protection Regulation (GDPR) in 2018 led us to study the potential impacts on pricing models. By applying anonymization methods on pure premium calculation models in non-life insurance, we explored different generalization approaches based on unsupervised learning. Finally, as the regulation also imposes criteria in terms of model explanation, we conclude with a general study of the methods that allow today to better understand complex methods such as neural networks.

The human lifespan has been increasing in the world for the last few centuries. This increase has been greater than predicted by specialists who have set limits. Despite significant uncertainties about the future of longevity, the biology of aging and its applications seem to be on the way to lowering mortality rates in old age, similar to the drop in infant mortality rates 150 years ago. The pharmaceutical industry is becoming aware of the potential of biomedical innovations stemming from the biology of aging, buying up biotechs and developing in-house teams. However, the actuarial tables, like the Lee Carter model, tend to predict an artificial deceleration of longevity and the calculated risks are far from representing major advances in the biology of aging. Future mortality models are developed here without producing this deceleration. It appears that an increase of about one quarter per year has so far been a better predictor than the trends in each country. Other models predict accelerations. We estimate the impacts on pensions. Ongoing pharmaceutical efforts to apply the results of biomedical research can be feared because of their impacts on pensions. We study the extent to which a longevity mega-fund can both help finance funded pensions and a large number of pharmaceutical developments: the pooling of clinical risks can financially capture longevity-related biomedical successes.

Artificial Intelligence is present in every aspect of our lives in the era of Big Data. It has led to revolutionary changes in various sectors, including e-commerce and finance. In this thesis, we present four applications of AI that improve existing goods and services, enable automation, and dramatically increase the efficiency of many tasks in both fields. First, we improve the product search service offered by most e-commerce sites by using a novel term weighting system to better evaluate the importance of terms in a search query. Next, we build a predictive model on daily sales using a time series forecasting approach and leverage the predicted results to rank product search results to maximize a company's revenue. Next, we propose the difficulty of online product classification and analyze winning solutions, consisting of state-of-the-art classification algorithms, on our real-world dataset. Finally, we combine the skills previously learned from time series-based sales prediction and classification to predict one of the most challenging but attractive time series: inventory. We perform an in-depth study on each stock in the S&P 500 Index using four state-of-the-art classification algorithms and report very promising results.

In this paper, we investigate the impact of the claim reporting strategy of drivers, within a bonus malus system. We exhibit the induced modification of the corresponding class level transition matrix and derive the optimal reporting strategy for rational drivers. The hunger for bonuses induces optimal thresholds under which, drivers do not claim their losses. A numerical algorithm is provided for computing such thresholds and realistic numerical applications are discussed.

This paper provides a meta-analysis of 1651 point estimates of Feldstein and Horioka saving retention coefficient from 49 peer-reviewed papers published over three decades. We get two main results. First, correcting for publication bias, we find a consistent underlying coefficient lying between 0.56 and 0.67 for studies using the original paper. Second, heterogeneity reported in the estimates of the Feldstein and Horioka can be explained by a few main factors. In particular, we find evidence that the saving retention coefficient is systematically underestimated with models written in first difference, models using the saving ratio or the current account ratio as the dependent variable instead of the investment ratio, and models including indicators of the public deficit or indicators of the country size as additional explanatory variables.

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In a life insurance market in French-speaking sub-Saharan Africa that is lagging behind but has a bright future if endogenous technical and commercial solutions emerge, the thesis proposes theoretical and operational tools adapted to its development. This approach is in line with the actions undertaken by the regional supervisory authority (CIMA) to provide the region's insurers with appropriate tools. Indeed, CIMA has initiated work on the construction of new regulatory experience tables, which has provided reliable and relevant references for the mortality of the insured population in the region. However, some useful technical issues were not developed in this construction work. The thesis therefore gives them special attention. Thus, on the one hand, the thesis provides tools to account for differences in mortality between countries in the region, while limiting the systematic risks associated with sampling fluctuations (due to small data sample sizes per country). In particular, it appears that if independent modeling of each country is not appropriate, heterogeneity models with observable factors, such as the Cox or Lin and Ying model, can achieve this goal. However, it should be noted that these heterogeneity models do not eliminate the systematic risk of sampling fluctuations in the estimation of the model, but only reduce this risk while increasing the systematic risk of model selection. On the other hand, the thesis also provides tools to model future experience mortality in the region. In the absence of data on past trends in experience mortality, neither the classical Lee-Carter model nor its extensions are applicable. A solution based on a parametric adjustment, an assumption on the shape of the evolution of the mortality level (linear or exponential evolution) and an expert opinion on the generational life expectancy at a given age is then proposed (this work is based on the Bongaarts model). Then, in a second step, assuming the availability of data on past trends (which for the record is not the case at this stage in the region, but should be in the next few years), the thesis proposes a modeling of future mortality from an external mortality reference and an analysis of the associated systematic risks (risks related to sampling fluctuations and the choice of the mortality reference)

This thesis focuses on bounding theorems for copulae. The first chapter is a survey of dependence and standard results on copulae, with applications to finance and insurance. The second chapter studies changes in the dependence structure in survival models and obtains limiting results using a bivariate concept of regular directional variation in high dimensions. Using some fixed point theorems, invariant copulae is exposed. Further on, it is proved that the Clayton copula is the only one invariant by truncation. In chapter 3-5 is studied the particular case of Archimedean copulae. The study in upper and lower is conducted and the restriction theorems are obtained. Chapter 6 tries to link the standard approach in extreme values and the one presented here, based on conditional copulae, i.e. obtained with joint exceedances. Chapter 7 focuses nonparametric (kernel based) on copula density evaluations, using the transformed kernel approach and beta kernels. And finally, a final chapter (a bijgevoegde stelling) focuses on temporal dependencies for natural events and studies the notion of return period where the observations are not independent. We consider some applications, on storm winds and heat waves (using GARMA processes, with long memory) and on flood events using the extension of ACD models, presented for high frequency financial data.

This thesis deals with the study of dependencies between risks, using copulas. Taking into account the dependencies that can exist between risks has become crucial for risk managers, and the stakes can be colossal (risk of contagion - and chain bankruptcies - within a portfolio of risky bonds, or correlations between extreme risks in reinsurance - where several a priori independent risks are affected when a catastrophe occurs). A better knowledge of the dependency structures is then fundamental in order to propose an adequate modeling. Therefore, the emphasis in this thesis is on the deformation of copulas as a function of time, or in the tails of the distribution. The first part is devoted to the temporal deformation of copulas in a credit risk context. By introducing conditional copulas, it is thus possible to study the dependence between the lifetimes before default of an issuer, knowing that no default has been observed during a given time period. Fixed point theorems allow to obtain limit behaviors, and to obtain results on first-to-default, for example. The following chapters deal with the use of conditional copulas in the modeling of extreme risks. The theory of extremes in a multivariate framework has been traditionally done by modeling maxima by components. But the study by joint threshold crossing offers a much greater richness. In particular, the study in the upper and lower tail is presented in the case of Archimedean copulas, with emphasis on the characterizations of the cases of asymptotic independence, usually so difficult to apprehend. The last part deals with the nonparametric estimation of copula densities, where kernel estimators are studied, allowing to avoid edge effects traditionally unavoidable when estimating a density with compact support. In particular, techniques are used to correctly estimate the density in the tails of distributions, including with censored data. Finally, a bijgevoegde stelling concludes this thesis on the study of time dependence for climate risks. Long memory models are used to model the risk of storms and to estimate the return period of the August 2003 heat wave. Finally, high-frequency models (similar to those used in finance to model the prices of securities on a transaction-by-transaction basis) are used to model hydrological data, and to propose new estimates for the risk of flooding.