PLANCHET Frederic

The use of algorithms exploiting heterogeneous and often high-volume data has developed very rapidly in recent years, taking advantage of increasing computing capacity and data collected by GAFA. These techniques first appeared in the insurance world to meet management or marketing needs: dimensioning of call centers, customer selection, automated analysis of contractual clauses, automation of underwriting processes, etc. Even if a few old attempts can be spotted, it is only recently that actuaries have started to integrate data science techniques more systematically into their "toolbox" and have started to identify issues where these approaches could prove to be more efficient than the usual approaches. In this book, at the crossroads of actuarial and data science, you will find a state of the art of the use of these techniques for risk analysis and quantification. Intended for students, academics and practitioners, it aims to provide a working basis and lines of thought for an enlightened use of data science in actuarial science.

Maintaining retirement systems stability is nowadays a big challenge for all countries. Such sustainability is widely related to a set of time-varying elements that include population structure, longevity, employment, and affiliation to social security. For the case of Algeria, public retirement works according to the pay-as-you-go principle and equilibrium is maintained by public subsidy. But, population is now aging, and longevity is improving. The retired population is supposed to grow faster than the population at working age. Consequently, it will be harder to keep equality between retirement incomes and outcomes especially if we consider the weakness of the demand for social security among workers. The latter remains widely dependent on public employment. the employees of the private sector are less covered. In the present paper, we aim to simulate the future evolution of the demographic and economic factors affecting the stability of the Algerian retirement system in order to show their long-run effect. As a result, we found that it will be impossible to keep the retirement sustainability within its current design. The accelerating aging process imposes to undertake heavy reforms in the near future.

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This paper proposes a method for quantifying the effect of a qualitative explanatory variable on a quantitative response that is more flexible to use than the simple coefficient of a multiplicative GLM model. The objective is to have a measure that does not require the proportionality assumption of the GLM and that is completely uncorrelated with the effect of the other explanatory variables included in the model. The approach is illustrated using data on the cost of automobile claims, for which we seek to quantify the impact of the adjuster who assessed the claim on the amount of the assessment.

In the insurance sector, the latest regulatory developments and accounting standards are moving towards standardization of risk management within organizations. In this context, the main objective of my thesis is to propose different methodologies for risk assessment and analysis in this sector. The first part of this manuscript deals with the problem of individual provisioning in non-life. I propose adaptations of ensemblistic machine learning algorithms and of some performance metrics for estimating claim durations and ultimate claim expenses in the presence of right-censored data. The application of these methods to real data from loan contracts or group insurance contracts leads to better and more robust estimates of the considered parameters. The second part presents an approach for estimating a one-year shock on the Undertaking Specific Parameters of the life insurance module of pillar 1 of the Solvency II standard formula. The use of the American credibility (or limited variation credibility) allows the partial taking into account of the constraints of availability of experience data (volumetry and depth of history) when calibrating the shocks. As an illustration, I have applied this approach to the incidence and continuation (or reinstatement) risks of disability and out-of-work benefits in a portfolio of loan contracts. The results obtained show significant decreases in the solvency capital requirements (SCR) of the underwriting risk compared to the standard formula. The third part is a descriptive study of the calculations of the standard formula for the evaluation of the economic capital requirement of the dependency risk. It highlights the shortcomings of the standard and suggests ways to improve it in order to better take into account the specificities of this risk. Finally, in the last part of the manuscript, I propose a comparative study of the preferences of attitudes towards risk in the financial sector, in particular banking and insurance. This is an empirical analysis conducted in three geographical areas (America, Europe and Africa) in order to measure the links and differences between risk attitude profiles and certain socio-demographic variables.

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In this paper, we implement a stochastic deflator with five economic and financial risk factors: interest rates, market price of risk, stock prices, default intensities, and convenience yields. We examine the deflator with different financial assets, such as stocks, zero‐coupon bonds, vanilla options, and corporate coupon bonds. We find required regularity conditions to implement our stochastic deflator. Our numerical results show the reliability of the deflator approach in pricing financial derivatives.

Long Term Care insurance contracts are complex insurance products covering an individual for which pricing and reserving issues are traditionally addressed by the introduction of multi-state models. This type of model allows one to describe the transitions of each insured through different states that correspond to events determining, under the terms of the contract, the respective commitments of the parties. The description of insurance contracts through multi-state models is the subject of several studies in the actuarial literature (cf. [21, 31] or [14]). To implement this approach to pricing or reserving, actuaries need to establish suitable statistical bases.

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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.

Pension funds that handle retirement risk need to invest assets in a diversified manner, on long durations and if possible while facing interest rate and longevity risk. In the recent years, a new class of investment called a longevity megafund was described, that invests in clinical trials for solutions against age-related diseases. Using simple models, we here study the financial interest for pension funds of investing in a longevity megafund.

Pension funds that handle retirement risk need to invest assets in a diversified manner, on long durations and if possible while facing interest rate and longevity risk. In the recent years, a new class of investment called a longevity megafund was described, that invests in clinical trials for solutions against age-related diseases. Using simple models, we here study the financial interest for pension funds of investing in a longevity megafund.

Yield losses due to climate are positively correlated. This goes against the principles of insurance and exposes the insurer to financial risks that he cannot bear alone. Reinsurers themselves may be overwhelmed by the sums involved. The financial markets, on the other hand, have the required financial capacity and the diversifying effect of climate risks could interest investors. A systemic risk management strategy consisting of isolating the correlated part of the return risk and transferring it to the financial markets via catastrophe bonds is analyzed in three points. First, pricing models isolating the systemic part of the risk are presented. Second, the low correlation of an agricultural bond is demonstrated, as well as its high returns, confirming its potential for investors. Finally, the evolution of the market value of companies issuing catastrophe bonds is studied. Overall, no impact is detected. In detail, repeated issuance favors the increase of the issuer's value, and large issuance favors the decrease. Index insurance is used as a support for the study. Based on return proxies rather than actual returns, they provide access to comprehensive and reliable databases. This work contributes to the limited literature on agricultural risks and their transfer to financial markets. It provides insurers with an alternative risk transfer strategy and opens the way to innovative investment tools.

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As more and more people believe that significant life extensions may come soon, should commonly used future mortality assumptions be considered prudent? We find here that commonly used actuarial tables for annuitants – as well as the Lee-Carter model – do not extrapolate life expectancy at the same rate for future years as for past years. instead they produce some longevity deceleration. This is typically because their mortality improvements decrease after a certain age, and those age-specific improvements are constant over time. As potential alternatives i) we study the Bongaarts model that produces straight increases in life expectancy. ii) we adapt it to produce best-practice longevity trends iii) we compare with various longevity scenarios even including a model for “life extension velocity”. iv) after gathering advances in biogerontology we discuss elements to help retirement systems resist to a potential strong increase in life expectancy.

The ORSA Own Risk Solvency and Assessment is a set of rules defined by the European Solvency II directive. It is intended to serve as a decision support tool and strategic risk analysis. In the context of the ORSA, insurance companies must assess their future solvency, on an ongoing and prospective basis. In order to do so, they must obtain projections of their balance sheet (assets and liabilities) over a certain time horizon. In this thesis, we focus mainly on the aspect of predicting future asset values. More precisely, we deal with the yield curve, its construction and extrapolation at a given date, and its predictions envisaged in the future. In the text, we refer to the "yield curve", but it is in fact the construction of discount factor curves. Counterparty default risk is not explicitly addressed, but techniques similar to those developed can be adapted to the construction of rate curves incorporating counterparty default risk.

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This paper focuses on the construction of incidence laws for total loss of autonomy over the period 2010-2012 using data from national hospitalization databases (PMSI 2008-2013). Our results are decomposed according to two types of dependence: cognitive dependence (or dementia) and physical dependence. Women have a slightly higher risk of entering dementia, whereas the risk for physical dependence is higher for men. The incidence of all-cause dependence is comparable between men and women. The results suggest a slowing down of the incidence beyond the age of 90 and a convergence of men and women at older ages. The implications of these results for extrapolation to older ages are discussed.

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Studying Long Term Care (LTC) insurance requires modeling the lifetime of individuals in presence of both terminal and non-terminal events which are concurrent. Although a nonhomogeneous 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 possible to derive asymptotic results for these probabilities under non-dependent random right-censorship, obtained 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.

This paper focuses on the construction of incidence laws for total loss of autonomy over the period 2010-2012 using data from national hospitalization databases (PMSI 2008-2013). Our results are decomposed according to two types of dependence: cognitive dependence (or dementia) and physical dependence. Women have a slightly higher risk of entering dementia, whereas the risk for physical dependence is higher for men. The incidence of all-cause dependence is comparable between men and women. The results suggest a slowing down of the incidence beyond the age of 90 and a convergence of men and women at older ages. The implications of these results for extrapolation to older ages are discussed.

Studying Long Term Care (LTC) insurance requires modeling the lifetime of individuals in presence of both terminal and non-terminal events which are concurrent. Although a nonhomogeneous 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 possible to derive asymptotic results for these probabilities under non-dependent random right-censorship, obtained 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.

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Technical risk management in French-speaking sub-Saharan Africa is a notion that is often absent in practice. Indeed, in this zone, it is very easy to find banks, insurance companies and pension institutions conducting their activities without integrating risk1 into their core management. This situation explains, a priori, the absence of reliable databases for quantitative studies. This thesis, which is complementary to the work of Kamega A2., focuses on the design of relevant actuarial tools adapted to the technical management of risks in French-speaking sub-Saharan Africa, which can be used by the governments of this zone as well as in the insurance and banking industries. In view of the progressive development of the countries in the CIPRES zone, we believe that the economic scenario generator (ESG) is the common tool for the technical management of risks related to the activities of governments and the banking and insurance industry. Note that the ESG is a tool capable of projecting economic and financial variables into a coherent system. This rich information will allow, for example, the governments of these countries to elaborate their budgets, to mobilize resources on the local financial market and to technically manage public debt. In the context of the design of the GSE, the contribution of this thesis consists in first specifying mathematical models, adapted to the context of the CIPRES zone, covering a large number of economic and financial variables. In a second step, calibration methods are presented in the context of absence of data (expert opinion) or presence of data (statistical approaches). Particular attention is paid to the extension of the GSE in order to take into account the future needs of professionals in the CIPRES area. This thesis also gives importance to the application of the GSE in the development of CIPRES countries through the contribution of the yield curve in the analysis and the conduct of monetary policy, the forecasting of economic and financial quantities, the estimation of implicit default probabilities and recovery rates of States and companies in a context of rating in local currency and the application of the Basel II/III framework in 2018. In the context of pension plans, these actuarial tools are useful in determining the parameters for steering the plan, in particular the "best estimate" valuation of the plan's liabilities, the financing and the asset allocation strategy.

Data quality is an overarching concern when it comes to building a mortality model or prospective mortality tables. This is even more significant when these procedures are based on a small population, as data may show major random fluctuations due to a lack of information for particular ages. Such situations arise frequently with the entry into force of Solvency II as insurers shall consider their own data sets, limited in size, to build best estimate tables. Since parametric methods are too rough to capture a realistic mortality pattern in two dimensions, the mortality profile is quite often adjusted using exogenous information, such as a table based on a national population. In light of this, the aim of this paper is to discuss the problem of choosing appropriate estimators for two-dimensional mortality rates or death rates in the presence of independent censoring. Indeed, practitioners currently use the Hoem estimator or the Kaplan-Meier estimator split by generation without questioning their relevance and reliability. We propose in this paper a comparative analysis of these estimators and try to give some criteria to choose one approach over another, and give some figures based on a real insurance portfolio and simulated data. Finally, we provided some non-parametric estimators for a direct estimation of death rates both with the cohort and the period approaches.

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A major challenge for modern societies, the loss of autonomy in the elderly, also known as dependence, is defined as a state of inability to perform all or part of the Acts of Daily Living (ADL) alone. It appears in the vast majority of cases under the effect of chronic pathologies related to aging. Faced with the significant costs associated with this condition, private insurers have developed a range of products to supplement public assistance. To quantify the risk, a multi-state model is used and the question arises of estimating the transition probabilities between the states (autonomy, death and one or more levels of dependence). Under the Markov hypothesis, these depend only on the current state, an assumption that is too restrictive to account for the complexity of the dependency process. In the more general semi-Markovian framework, these probabilities also depend on the time spent in the current state. In this thesis, we study the need for a semi-Markovian modeling of the process. We highlight the impact of the time spent in dependency on the probabilities of death. We also show that taking into account the diversity induced by the pathologies allows us to improve significantly the adequacy of the proposed model to the studied data. Moreover, we establish that the particular shape of the probability of death as a function of the time spent in dependency can be explained by the mixture of the groups of pathologies that constitute the population of dependent individuals.

As more and more people believe that significant life extensions may come soon, should commonly used future mortality assumptions be considered prudent? We find here that commonly used actuarial tables for annuitants – as well as the Lee-Carter model – do not extrapolate life expectancy at the same rate for future years as for past years. instead they produce some longevity deceleration. This is typically because their mortality improvements decrease after a certain age, and those age-specific improvements are constant over time. As potential alternatives i) we study the Bongaarts model that produces straight increases in life expectancy. ii) we adapt it to produce best-practice longevity trends iii) we compare with various longevity scenarios even including a model for “life extension velocity”. iv) after gathering advances in biogerontology we discuss elements to help retirement systems resist to a potential strong increase in life expectancy.

The present article illustrates an approach to construct prospective mortality tables for which the data available are composed by heterogeneous groups observed during different periods. Without explicit consideration of heterogeneity, it is necessary to reduce the period of observation at the intersection of the different populations observation periods. This reduction of the available history can arm the determination of the mortality trend and its extrapolation. We propose a model taking explicitly into account the heterogeneity, so as to preserve the entire history available for all populations. We use local kernel-weighted log-likelihood techniques to graduate the observed mortality. The extrapolation of the smoothed surface is performed by identifying the mortality components and their importance over time using singular values decomposition. Then time series methods are used to extrapolate the time-varying coefficients. We investigate the divergences in the mortality surfaces generated by a number of previously proposed models on three levels. These concern the proximity between the observations and the model, the regularity of the fit as well as the plausibility and consistency of the mortality trends.

The Solvency 2 advent and the best-estimate methodology in future cash-flows valuation lead insurers to focus particularly on their assumptions. In mortality, hypothesis are critical as insurers use best-estimate laws instead of standard mortality tables. Backtesting methods, i.e. ex-post modelling validation processes , are encouraged by regulators and rise an increasing interest among practitioners and academics. In this paper, we propose a statistical approach (both parametric and non-parametric models compliant) for mortality laws backtesting under model risk. Afterwards, a specification risk is introduced assuming that the mortality law is subject to random variations. Finally, the suitability of the proposed method will be assessed within this framework.

This paper provides an overview of pension systems in French-speaking sub-Saharan Africa. Generally, pension systems are designed for the formal sector (government employees, private sector employees and certain specific trades). However, numerous reforms have been carried out with the main objective of reducing the financial deficit of these pension schemes and extending social protection to the self-employed (informal sector). In this article, we will first look at the pension context in the CIPRES zone. In this section, we will focus on the challenges facing pension systems, the economic and social context and the organization of the pension system. Secondly, we will analyze the existing pension systems of some countries in the CIPRES zone. In practice, we will discuss the insured population, the technical management (financial burden, financing and asset allocation), as well as the reforms (if any) made to the schemes to ensure their long-term sustainability. Finally, in the conclusion, we will make recommendations that could help ensure the technical management of pension plans over the long term. These three parts will allow us to place the subject in its context in order to understand the problem of retirement in the CIPRES zone.

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This paper presents a model for the determination and forecast of the number of defaults and credit changes by estimating a reduced-form ordered regression model with a large data set from a credit insurance portfolio. Similarly to banks with their classical credit risk management techniques, credit insurers measure the credit quality of buyers with rating transition matrices depending on the economical environment. Our approach consists in modeling stochastic transition matrices for homogeneous groups of firms depending on macroeconomic risk factors. One of the main features of this business is the close monitoring of covered firms and the insurer’s ability to cancel or reduce guarantees when the risk changes. As our primary goal is a risk management analysis, we try to account for this leeway and study how this helps mitigate risks in case of shocks. This specification is particularly useful as an input for the Own Risk Solvency Assessment (ORSA) since it illustrates the kind of management actions that can be implemented by an insurer when the credit environment is stressed.

The implementation of Solvency II leads actuaries to question the good adequacy between models and data. Therefore, this thesis aims to study several statistical approaches, often unknown to practitioners, allowing the use of multi-state methods to model and manage individual risks in insurance. Chapter 1 presents the general context of this thesis and positions its main contributions. We discuss the basic concepts related to the use of multi-state models in insurance and describe the classical inference techniques adapted to the data encountered, whether Markovian or non-Markovian. Finally, we present how these models can be used for credit risk management. Chapter 2 focuses on the use of non-parametric inference methods for the construction of incidence laws in LTC insurance. Since several input causes are likely to be involved and of interest to actuaries, we focus on a method used for estimating continuous-time Markovian multi-state models. We then compare these estimators to those classically used by survival analysis practitioners. This second approach can have significant biases because it does not allow to correctly understand the possible interaction between the causes. In particular, it includes an independence hypothesis that cannot be tested in the context of competing risks models. Our approach then consists in measuring the error made by practitioners when constructing incidence laws. A numerical application is then considered on the basis of data from a long term care insurer.

This article presents an operational framework for constructing and validating projected mortality table specific to an insurer. We describe several methods of increasing complexity and the process of validation allowing an insurer to adjust a baseline mortality to get closer to a best estimate assessment of its mortality and longevity risk. They provide to the insurer some latitude of choice while preserving simplicity of implementation for the basic methodology. The methodologies articulate around an iterative procedure allowing to choose parsimoniously the most satisfying one. The process of validation is assessed on three levels. This concerns the proximity between the observations and the model, the regularity of the fit as well as the plausibility and consistency of the mortality trends. Finally, the procedure is illustrated from experience data originating from a French Insurance portfolio.

In this paper, we focus on uncertainty issues on disabled lives survival probabilities of LTC insurance policyholders and its consequences on solvency capital requirement. Among the risks affecting long-term care portfolios, special attention is addressed to the table risk, i.e. the risk of unanticipated aggregate mortality, arising from the uncertainty in modeling LTC claimants survival law. The table risk can be thought as the risk of systematic deviations referring not only to a parameter risk but, as well, to any other sources leading to a misinterpretation of the life table resulting for example from an evolution of medical techniques or a change in rules of acceptance. In fine, the idea is to introduce the risk of systematic deviations arising from the uncertainty on the disabled lives death probabilities directly. We analyze the consequences of an error of appreciation on the disabled lives survival probabilities in terms of level of reserves and describe a framework in an Own Risk and Solvency Ass.

The Solvency 2 prudential framework, which will come into force at the beginning of 2016, imposes an instantaneous and highly analytical view of the risks carried in order to determine the minimum capital requirement ("pillar 1") that an insurer must hold. While this approach has the advantage of providing a normative framework as well as a certain exhaustiveness of analysis, in practice it leads to the design of models that are ill-suited to the multi-year projection of the balance sheet and solvency because they are not sufficiently robust. Additional analyses ("pillar 2"), which aim to measure the impact of the strategic plan and management actions on the insurer's solvency, are also required. They are part of a more global approach allowing to provide adequate information on the deformation of the distribution of key balance sheet elements (net asset value, capital requirement, coverage ratio, etc.) over time for the steering of the organization. The challenge is then, on the basis of a global vision of the risks (pricing, provisioning, commercial, hedging and financial risks) to propose prospective models flexible enough to allow these projections as well as an analysis of the impact of the company's management actions. The objective of this book is to describe such approaches (model building and hypothesis justification) and to propose realistic illustrations. Its ambition is to provide a set of aggregated modeling tools for the insurer's balance sheet that are better able to account for dynamic aspects and thus provide a tool for operational management of the business.

The new Solvency 2 regulatory standards have a very important impact on credit insurance. The objective of this directive is that insurance companies better measure the different risks they face, so that they can build up sufficient capital to face crisis situations. Our work focuses on a rather specific insurance activity: credit insurance. Under Solvency 2, most credit insurers will move towards the development of internal models in order to better estimate their capital requirements. The objective of our study is to propose, or to give avenues for improvement of one type of internal model. First, we present a general overview of the credit insurance business and then we approach the subject of an internal model. We will then present the model we have chosen to use, a multifactor model associated with the Merton approach. We will also compare the methods for integrating correlations between counterparties in the Solvency 2 standards with that of the internal model. We will then try to refine the internal model in order to take into account an important characteristic of credit insurance: the management of guarantees (limits), which as we will see induces a decrease in capital requirements. To do so, we will introduce the consideration of credit cycles for the calculation of losses, a model that is no longer monoperiodic, as is usually the case, but with two periods. We will then present the results obtained with this model. We will then present an alternative approach using the piecewise linear approximation method via Monte Carlo simulations (PLMC). The aim here is to move from a discrete to a continuous model. We then compare the Gaussian and Student dependence structures to see what the change in this structure would mean for the capital requirements. Finally, we will look at the problem of finding high quantiles and studying the convergence of our variables. To do so, we will first introduce the measure of the market price of risk, and we will present an estimate of this market price of risk, more specifically for interest rate risk. This will allow us to obtain the dynamics of rates in a risk neutral universe. We will then address the issue of calculating the Best Estimate, in a framework of dependence between interest rate and credit risks. The calculation of the SCR will follow. We will discuss an alternative approach for calculating the capital requirement, an approach specific to structural models and which would make it possible to do without simulations for this calculation. Finally, we will conclude our study by exposing the different issues of this thesis as well as the contributions made, and the problems encountered during the work.

In this paper we present an analytical approximation of the best estimate of a savings contract. This approximation aims to provide a framework for robust and justifiable calculation of the own risk solvency assessment avoiding the complexity of direct approaches. A numerical application is proposed.

Business and credit cycles have an impact on credit insurance, as they do on other businesses. Nevertheless, in credit insurance, the impact of the systemic risk is even more important and can lead to major losses during a crisis. Because of this, the insurer surveils and manages policies almost continuously. The management actions it takes limit the consequences of a downturning cycle. However, the traditional modeling of economic capital does not take into account this important feature of credit insurance. This paper proposes a model aiming to estimate future losses of a credit insurance portfolio, while taking into account the insurer’s management actions. The model considers the capacity of the credit insurer to take on less risk in the case of a cycle downturn, but also the inverse, in the case of a cycle upturn. so, losses are predicted with a more dynamic perspective. According to our results, the economic capital is over-estimated when not considering the management actions of the insurer.

Our interest in this thesis is to combine the different techniques for measuring operational risk in the financial sectors, and we are particularly interested in the consequences of estimation risk in models, which is a particular operational risk. We will present the associated mathematical and actuarial concepts as well as a numerical application with respect to the advanced measurement approach as Loss Distribution to calculate the capital requirement. In addition, we focus on estimation risk illustrated with expert opinion scenario analysis in conjunction with internal loss data to assess our exposure to severity events. We conclude this first part by defining an OLS-based scaling technique that allows us to normalize our external data to a local Lebanese bank.In the second part, we give importance on the measurement of the error induced on the SCR by the estimation error of the parameters, we propose an alternative method to estimate a yield curve and we conclude by drawing attention on the reflections around the assumptions of calculation and what we agree to qualify as an assumption "consistent with market values" would be much more relevant and effective than the complexification of the model, source of additional instability, thus highlighting the estimation risk which is linked to the operational risk and must be given much more attention in our working models.

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This paper proposes to illustrate the implementation of non-parametric estimation methods, introduced in the framework of Markovian multi-state models with censoring, to construct laws of experience applicable in the presence of several concurrent events. This situation arises in practice in long term care insurance when it is necessary to distinguish the incidence laws by pathology. Therefore, rather than applying techniques usually used by practitioners and consisting in observing marginally each cause of entry into dependence, the approach described allows to estimate globally all the entry laws by cause and to correctly apprehend the interdependence between each of them. This work provides a comparison of the results obtained by these two approaches at the level of the provision to be made in order to justify a marginal approach, which is simpler to implement in practice.

We consider the problem of the global minimization of a function observed with noise. This problem occurs for example when the objective function is estimated through stochastic simulations. We propose an original method for iteratively partitioning the search domain when this area is a nite union of simplexes. On each subdomain of the partition, we compute an indicator measuring if the subdomain is likely or not to contain a global minimizer. Next areas to be explored are chosen in accordance with this indicator. Con dence sets for minimizers are given. Numerical applications show empirical convergence results, and illustrate the compromise to be made between the global exploration of the search domain and the focalization around potential minimizers of the problem.

We are interested in modeling the mortality of long-term care (LTC) claimants having the same level of severeness (heavy claimant). Practitioners often use empirical methods that rely heavily on expert opinions. We propose approaches not depending on an expert’s advice. We analyze the mortality as a function of both the age of occurrence of the claim and the duration of the care. LTC claimants are marked by a relatively complex mortality pattern. Hence, rather than using parametric approaches or models with expert opinions, adaptive local likelihood methods allow us to extract the information from the data more pertinently. We characterize a locally adaptive smoothing pointwise method using the intersection of confidence intervals rule, as well as a global method using local bandwidth correction factors. The latter is an extension of the adaptive kernel method proposed by Gavin et al. (1995) to likelihood techniques. We vary the amount of smoothing in a location-dependent manner and allow adjustments based on the reliability of the data. Tests, and single indices summarizing the lifetime probability distribution are used to compare the graduated series obtained by adaptive local kernel-weighted log-likelihoods to pp-spline and local likelihood models.

The Solvency 2 advent and the best-estimate methodology in future cash-flows valuation lead insurers to focus particularly on their assumptions. In mortality, hypothesis are critical as insurers use best-estimate laws instead of standard mortality tables. Backtesting methods, i.e. ex-post modelling validation processes, are encouraged by regulators and rise an increasing interest among practitioners and academics. In this paper, we propose a statistical approach (both parametric and non-parametric models compliant) for mortality laws backtesting under model risk. Afterwards, we'll introduce a specification risk supposing the mortality law true in average but subject to random variations. Finally, the suitability of our method will be assessed within this framework.

This thesis focuses on strategic asset allocation models and their application to the management of financial reserves in pay-as-you-go pension plans, particularly those that are partially funded. The study of the usefulness of reserves for a pay-as-you-go system and a fortiori their management remains a little explored subject. Conventional assumptions are sometimes considered too restrictive to describe the complex evolution of reserves. New models and results are developed at three levels: the generation of economic scenarios (GSE), numerical optimization techniques and the choice of the optimal strategic allocation in an asset-liability management (ALM) context. Within the framework of economic and financial scenario generation, some performance measurement indicators of the GSE have been studied. In addition, improvements have been made compared to what is usually done in the construction of the GSE, particularly in the choice of the correlation matrix between the modeled variables. Concerning the calibration of the GSE, a set of tools allowing the estimation of its different parameters has been presented. This thesis has also paid particular attention to the numerical techniques for finding the optimum, which remain essential issues for the implementation of an allocation model. A reflection on a global optimization algorithm for a non-convex and noisy function has been developed. The algorithm allows to easily modulate, by means of two parameters, the reiteration of draws in a neighborhood of the discovered solution points, or conversely the exploration of the function in unexplored areas. We then present innovative ALM techniques based on stochastic programming. Their application has been developed for the choice of the strategic asset allocation of partially funded pay-as-you-go pension plans. A new methodology for the generation of the scenario tree was adopted at this level. Finally, a comparative study of the developed ALM model with the one based on the Fixed-Mix strategy was performed. Various sensitivity tests were also carried out to measure the impact of changes in certain key input variables on the results produced by our ALM model.

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)

The present work is a follow-up to the doctoral thesis prepared in the Actuarial and Financial Sciences laboratory (SAF) of the University of Lyon 1 and defended on November 20, 2006 on the theme of the technical management of a life annuity plan: identification and measurement of risks, asset allocation, actuarial monitoring. He presents work on longevity risk and the determination of capital requirements in the context of Solvency 2.

Recent changes in regulatory and accounting systems as well as in market practices have led to a more detailed and segmented analysis of the risks borne by a life annuity plan. In this context, a revision of the classical modeling of such a plan is necessary, taking into account in particular on the liabilities side the risk associated with the uncertainty on the future mortality (stochastic mortality and model risk) and on the assets side the essentially discontinuous character of the prices of the assets in which the plan invests its assets This work defines the broad lines of an asset/liability model of a life annuity plan that takes these constraints into account.