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Ce livre est consacré à la modélisation et à l'évaluation quantitative des risques en actuariat sur une période. Après un bref rappel des notions en théorie des probabilités, l'auteur présente les modèles de base en actuariat permettant de décrire le comportement des risques en assurance. La mutualisation et les méthodes d'agrégation de risques indépendants sont passées en revue tout comme les notions de base de simulation stochastique et les applications pour l'évaluation quantitative des risques. Une brève introduction aux ordres stochastiques univariés, utilisés pour comparer et expliquer q

Insurance --- Risk (Insurance) --- Mathematics. --- Business mathematics --- Actuarial science --- Risk

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Motivated by the many and long-standing contributions of H. Gerber and E. Shiu, this book gives a modern perspective on the problem of ruin for the classical Cramér–Lundberg model and the surplus of an insurance company. The book studies martingales and path decompositions, which are the main tools used in analysing the distribution of the time of ruin, the wealth prior to ruin and the deficit at ruin. Recent developments in exotic ruin theory are also considered. In particular, by making dividend or tax payments out of the surplus process, the effect on ruin is explored. Gerber-Shiu Risk Theory can be used as lecture notes and is suitable for a graduate course. Each chapter corresponds to approximately two hours of lectures.

Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Mathematics. --- Actuarial science. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Actuarial Sciences. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Statistics --- Insurance --- Math --- Science --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities

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Risk has been described in the past by a simple measure, such as the variance, and risk attitude is often considered simply a degree of risk aversion. However, this viewpoint is usually not sufficient. Risk Measures and Attitudes collects contributions which illustrate how modern approaches to both risk measures and risk attitudes are inevitably intertwined. The settings under which this is discussed include portfolio choice, mitigating credit risk and comparing risky alternatives. This book will be a useful study aid for practitioners, students and researchers of actuarial science and risk management.

financiële analyse --- stochastische analyse --- Probability theory --- toegepaste wiskunde --- wiskunde --- financieel management --- Operational research. Game theory --- kansrekening --- waarschijnlijkheidstheorie --- Financial analysis --- Mathematics --- Finance --- Quantitative methods (economics) --- Risk (Insurance) --- Risk management --- Risque (Assurance) --- Gestion du risque --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Finance. --- Mathematics. --- Distribution (Probability theory. --- Actuarial Sciences. --- Quantitative Finance. --- Applications of Mathematics. --- Probability Theory and Stochastic Processes. --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Funding --- Funds --- Economics --- Currency question --- Financial risk. --- Actuarial science. --- Economics, Mathematical . --- Applied mathematics. --- Engineering mathematics. --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematical economics --- Econometrics --- Statistics --- Insurance --- Methodology

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The author's particular interest in the area of risk measures is to combine this theory with the analysis of dependence properties. The present volume gives an introduction of basic concepts and methods in mathematical risk analysis, in particular of those parts of risk theory that are of special relevance to finance and insurance. Describing the influence of dependence in multivariate stochastic models on risk vectors is the main focus of the text that presents main ideas and methods as well as their relevance to practical applications. The first part introduces basic probabilistic tools and methods of distributional analysis, and describes their use to the modeling of dependence and to the derivation of risk bounds in these models. In the second, part risk measures with a particular focus on those in the financial and insurance context are presented. The final parts are then devoted to applications relevant to optimal risk allocation, optimal portfolio problems as well as to the optimization of insurance contracts. Good knowledge of basic probability and statistics as well as of basic general mathematics is a prerequisite for comfortably reading and working with the present volume, which is intended for graduate students, practitioners and researchers and can serve as a reference resource for the main concepts and techniques.  .

Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Distribution (Probability theory. --- Finance. --- Mathematics. --- Statistics. --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Actuarial Sciences. --- Applications of Mathematics. --- Operations Research, Management Science. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Math --- Science --- Funding --- Funds --- Economics --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probabilities. --- Economics, Mathematical . --- Actuarial science. --- Applied mathematics. --- Engineering mathematics. --- Operations research. --- Management science. --- Statistics . --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Engineering --- Engineering analysis --- Statistics --- Insurance --- Mathematical economics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology