En été 2013, le terme de "Big Data" fait son apparition et suscite un fort intérêt auprès des entreprises. Cette thèse étudie ainsi l'apport de ces méthodes aux sciences actuarielles. Elle aborde aussi bien les enjeux théoriques que pratiques sur des thématiques à fort potentiel comme l'textit{Optical Character Recognition} (OCR), l'analyse de texte, l'anonymisation des données ou encore l'interprétabilité des modèles. Commençant par l'application des méthodes du machine learning dans le calcul du capital économique, nous tentons ensuite de mieux illustrer la frontrière qui peut exister entre l'apprentissage automatique et la statistique. Mettant ainsi en avant certains avantages et différentes techniques, nous étudions alors l'application des réseaux de neurones profonds dans l'analyse optique de documents et de texte, une fois extrait. L'utilisation de méthodes complexes et la mise en application du Réglement Général sur la Protection des Données (RGPD) en 2018 nous a amené à étudier les potentiels impacts sur les modèles tarifaires. En appliquant ainsi des méthodes d'anonymisation sur des modèles de calcul de prime pure en assurance non-vie, nous avons exploré différentes approches de généralisation basées sur l'apprentissage non-supervisé. Enfin, la réglementation imposant également des critères en terme d'explication des modèles, nous concluons par une étude générale des méthodes qui permettent aujourd'hui de mieux comprendre les méthodes complexes telles que les réseaux de neurones / In summer 2013, the term "Big Data" appeared and attracted a lot of interest from companies. This thesis examines the contribution of these methods to actuarial science. It addresses both theoretical and practical issues on high-potential themes such as textit{Optical Character Recognition} (OCR), text analysis, data anonymization and model interpretability. Starting with the application of machine learning methods in the calculation of economic capital, we then try to better illustrate the boundary that may exist between automatic learning and statistics. Highlighting certain 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 its potential impacts on pricing models. By applying anonymization methods to pure premium calculation models in non-life insurance, we explored different generalization approaches based on unsupervised learning. Finally, as regulations also impose criteria in terms of model explanation, we conclude with a general study of methods that now allow a better understanding of complex methods such as neural networks

A pension plan administrator promises certain benefits in the future in exchange for labor today. In order to budget for this expense and create more security for the participant, the administrator uses a pension cost method. Each cost method assigns a portion of the future liability to the current year. This is called the normal cost. We calculate the normal cost under three cost methods using different annuity, interest and inflation assumptions. Then we make comparisons between cost methods as well as between assumption changes. The cost methods considered in this paper are the unit credit cost method, projected unit credit cost method, and the entry age cost method. Both the constant dollar and the constant percent versions of the entry age cost method are considered.

Industrial Life Insurance (ILI) was introduced in Sweden in the beginning of the 1900s. Following models already used in the United Kingdom and the United States, this insurance was specifically aimed at manual labourers, promising pension savings and compensation to surviving relatives. The insurance was an immediate success, with almost three million insurance policies in force by the mid-1900s. ILI was characterised by extensive and carefully monitored marketing practices. By managing an army of agents, the companies sold policies and collected premiums on a regular basis in the homes of the insured. The purpose of the dissertation is to analyse the development of a commercial business with social policy aspirations, and how it interacted with other social security institutions. How could ILI thrive in the emerging Swedish welfare state that, according to existing research, allowed little space for market-based welfare alternatives? The dissertation also seeks to contribute to a broader understanding of the contemporary “welfare market” in Sweden today. From a perspective of welfare formation as a social process, the emergence and expansion of ILI is interpreted as a phenomenon that has shaped, and been shaped by, the social policy arena. The insurance industry’s capacity to adapt to the changing ambitions of the state in this arena is emphasised. Furthermore, its leading representatives’ ability to continuously locate the role of life insurance in the shifting landscape of social policy is underlined. By locating welfare in separate but complementary public and private spheres, the industry contributed to the shaping of the compulsory pension scheme introduced in 1913 and the overall regulation of insurance in the mid-twentieth century. The social security of Swedish citizens was now to be ensured according to the vision of complementary spheres that the insurance industry had advocated for almost fifty years. The insurance companies’ commercial activities are analysed as a form of governmentality, where the agency system is scrutinized as an interventionist practice that created a long lasting relationship between the companies and the working classes. The dissertation shows how the industrialists’ role as “insurance experts” was used to influence public policies. As public figures and experts on various committees, representatives of the industry advocated a welfare formation that left ample space for their own business interests. The scientisation of security was also essential in creating a product where social aspirations and commercial logics could be united. The success of ILI thus rested on the interaction with the state apparatus. An arena of social policy was established where commercial companies were to be the supplier of all welfare above the level of “meagre basic security”. Through intense marketing measures, commercial actors influenced the perceptions of security and welfare. The process of welfare formation led to the internalisation of commercial ideals about social security that now constitutes an essential dimension of the Swedish welfare state.

O sistema de fundos de pensão possui papel fundamental na constituição de poupança e desenvolvimento do mercado financeiro e de capitais de um país. As incertezas de sustentabilidade do equilíbrio financeiro no longo prazo direcionam a exigência de uma supervisão robusta sobre os diversos riscos incorridos, não se restringindo apenas ao seu estado de solvência. A presente dissertação procura apresentar modelos baseados na avaliação dos riscos de um fundo de pensão, passando pela situação atuarial, as características dos planos, bem como pelos parâmetros relacionados ao mercado de capitais e formas de gestão dos investimentos. Os modelos propostos nos ajudam a visualizar o risco atuarial justificado pelo aumento da expectativa de vida, o risco de mercado através do reinvestimento e o risco de mercado em função do nível das taxas de juros. Ainda, tendo em conta estes riscos quantificáveis, é efetuada uma aplicação prática com o objetivo de determinação do requisito de capital de um determinado fundo de pensão para a cobertura destes riscos, tendo por base o modelo do projeto europeu de Solvência II, desenvolvido no âmbito da atividade seguradora. / The system of pension funds has a primary role in the formation of savings and financial market development and capital of a country. The uncertainties of financial balance sustainability in the long term drive the requirement for a robust supervision on the various risks involved, not restricted only to its state of solvency. This dissertation seeks to present models based on risk assessment of a pension fund, through the actuarial situation, the characteristics of the plans, as well as the parameters related to capital markets and ways of managing investments. The proposed models help us to see the actuarial risk justified by the increase in life expectancy, market risk through reinvestment and market risk based on the level of interest rates. Still, considering these risks quantifiable, a practical application is made for the purpose of determining the capital requirement of a particular pension fund to cover these risks, based on the model of the European Solvency II project, developed within the ambit of insurance activity.

O sistema de fundos de pensão possui papel fundamental na constituição de poupança e desenvolvimento do mercado financeiro e de capitais de um país. As incertezas de sustentabilidade do equilíbrio financeiro no longo prazo direcionam a exigência de uma supervisão robusta sobre os diversos riscos incorridos, não se restringindo apenas ao seu estado de solvência. A presente dissertação procura apresentar modelos baseados na avaliação dos riscos de um fundo de pensão, passando pela situação atuarial, as características dos planos, bem como pelos parâmetros relacionados ao mercado de capitais e formas de gestão dos investimentos. Os modelos propostos nos ajudam a visualizar o risco atuarial justificado pelo aumento da expectativa de vida, o risco de mercado através do reinvestimento e o risco de mercado em função do nível das taxas de juros. Ainda, tendo em conta estes riscos quantificáveis, é efetuada uma aplicação prática com o objetivo de determinação do requisito de capital de um determinado fundo de pensão para a cobertura destes riscos, tendo por base o modelo do projeto europeu de Solvência II, desenvolvido no âmbito da atividade seguradora. / The system of pension funds has a primary role in the formation of savings and financial market development and capital of a country. The uncertainties of financial balance sustainability in the long term drive the requirement for a robust supervision on the various risks involved, not restricted only to its state of solvency. This dissertation seeks to present models based on risk assessment of a pension fund, through the actuarial situation, the characteristics of the plans, as well as the parameters related to capital markets and ways of managing investments. The proposed models help us to see the actuarial risk justified by the increase in life expectancy, market risk through reinvestment and market risk based on the level of interest rates. Still, considering these risks quantifiable, a practical application is made for the purpose of determining the capital requirement of a particular pension fund to cover these risks, based on the model of the European Solvency II project, developed within the ambit of insurance activity.

The aim of this thesis is to develop algorithmic methods for computing particular performance measures of interest for a general class of discrete-based insurance risk models. We build upon and generalize the insurance risk models considered by Drekic and Mera (2011) and Alfa and Drekic (2007), by incorporating a threshold-based dividend system in which dividends only get paid provided some period of good financial health is sustained above a pre-specified threshold level. We employ two fundamental methods for calculating the performance measures under the more general framework. The first method adopts the matrix-analytic approach originally used by Alfa and Drekic (2007) to calculate various ruin-related probabilities of interest such as the trivariate distribution of the time of ruin, the surplus prior to ruin, and the deficit at ruin. Specifically, we begin by introducing a particular trivariate Markov process and then expressing its transition probability matrix in a block-matrix form. From this characterization, we next identify an initial probability vector for the process, from which certain important conditional probability vectors are defined. For these vectors to be computed efficiently, we derive recursive expressions for each of them. Subsequently, using these probability vectors, we derive expressions which enable the calculation of conditional ruin probabilities and, from which, their unconditional counterparts naturally follow. The second method used involves the first claim conditioning approach (i.e., condition on knowing the time the first claim occurs and its size) employed in many ruin theoretic articles including Drekic and Mera (2011). We derive expressions for the finite-ruin time based Gerber-Shiu function as well as the moments of the total dividends paid by a finite time horizon or before ruin occurs, whichever happens first. It turns out that both functions can be expressed in elegant, albeit long, recursive formulas. With the algorithmic derivations obtained from the two fundamental methods, we next focus on computational aspects of the model class by comparing six different types of models belonging to this class and providing numerical calculations for several parametric examples, highlighting the robustness and versatility of our model class. Finally, we identify several potential areas for future research and possible ways to optimize numerical calculations.

The research on optimal reinsurance design dated back to the 1960’s. For nearly half a century, the quest for optimal reinsurance designs has remained a fascinating subject, drawing significant interests from both academicians and practitioners. Its fascination lies in its potential as an effective risk management tool for the insurers. There are many ways of formulating the optimal design of reinsurance, depending on the chosen objective and constraints. In this thesis, we address the problem of optimal reinsurance designs from an insurer’s perspective. For an insurer, an appropriate use of the reinsurance helps to reduce the adverse risk exposure and improve the overall viability of the underlying business. On the other hand, reinsurance incurs additional cost to the insurer in the form of reinsurance premium. This implies a classical risk and reward tradeoff faced by the insurer. The primary objective of the thesis is to develop theoretically sound and yet practical solution in the quest for optimal reinsurance designs. In order to achieve such an objective, this thesis is divided into two parts. In the first part, a number of reinsurance models are developed and their optimal reinsurance treaties are derived explicitly. This part focuses on the risk measure minimization reinsurance models and discusses the optimal reinsurance treaties by exploiting two of the most common risk measures known as the Value-at-Risk (VaR) and the Conditional Tail Expectation (CTE). Some additional important economic factors such as the reinsurance premium budget, the insurer’s profitability are also considered. The second part proposes an innovative method in formulating the reinsurance models, which we refer as the empirical approach since it exploits explicitly the insurer’s empirical loss data. The empirical approach has the advantage that it is practical and intuitively appealing. This approach is motivated by the difficulty that the reinsurance models are often infinite dimensional optimization problems and hence the explicit solutions are achievable only in some special cases. The empirical approach effectively reformulates the optimal reinsurance problem into a finite dimensional optimization problem. Furthermore, we demonstrate that the second-order conic programming can be used to obtain the optimal solutions for a wide range of reinsurance models formulated by the empirical approach.

We propose a situation in which a single employee is responsible for processing incoming claims to an insurance company that can be classified as being one of two possible types. More specifically, we consider a priority-based system having separate buffers to store high priority and low priority incoming claims. We construct a mathematical model and perform queueing analysis to evaluate the performance of this priority-based system, which incorporates the possibility of claims being redistributed, lost, or prematurely processed.

The research on optimal reinsurance design dated back to the 1960’s. For nearly half a century, the quest for optimal reinsurance designs has remained a fascinating subject, drawing significant interests from both academicians and practitioners. Its fascination lies in its potential as an effective risk management tool for the insurers. There are many ways of formulating the optimal design of reinsurance, depending on the chosen objective and constraints. In this thesis, we address the problem of optimal reinsurance designs from an insurer’s perspective. For an insurer, an appropriate use of the reinsurance helps to reduce the adverse risk exposure and improve the overall viability of the underlying business. On the other hand, reinsurance incurs additional cost to the insurer in the form of reinsurance premium. This implies a classical risk and reward tradeoff faced by the insurer. The primary objective of the thesis is to develop theoretically sound and yet practical solution in the quest for optimal reinsurance designs. In order to achieve such an objective, this thesis is divided into two parts. In the first part, a number of reinsurance models are developed and their optimal reinsurance treaties are derived explicitly. This part focuses on the risk measure minimization reinsurance models and discusses the optimal reinsurance treaties by exploiting two of the most common risk measures known as the Value-at-Risk (VaR) and the Conditional Tail Expectation (CTE). Some additional important economic factors such as the reinsurance premium budget, the insurer’s profitability are also considered. The second part proposes an innovative method in formulating the reinsurance models, which we refer as the empirical approach since it exploits explicitly the insurer’s empirical loss data. The empirical approach has the advantage that it is practical and intuitively appealing. This approach is motivated by the difficulty that the reinsurance models are often infinite dimensional optimization problems and hence the explicit solutions are achievable only in some special cases. The empirical approach effectively reformulates the optimal reinsurance problem into a finite dimensional optimization problem. Furthermore, we demonstrate that the second-order conic programming can be used to obtain the optimal solutions for a wide range of reinsurance models formulated by the empirical approach.

We propose a situation in which a single employee is responsible for processing incoming claims to an insurance company that can be classified as being one of two possible types. More specifically, we consider a priority-based system having separate buffers to store high priority and low priority incoming claims. We construct a mathematical model and perform queueing analysis to evaluate the performance of this priority-based system, which incorporates the possibility of claims being redistributed, lost, or prematurely processed.