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This book provides a compact and systematic overview of closure properties of heavy-tailed and related distributions, including closure under tail equivalence, convolution, finite mixing, maximum, minimum, convolution power and convolution roots, and product-convolution closure. It includes examples and counterexamples that give an insight into the theory and provides numerous references to technical details and proofs for a deeper study of the subject. The book will serve as a useful reference for graduate students, young researchers, and applied scientists.

Probabilities. --- Distribution (Probability theory). --- Stochastic models. --- Actuarial science. --- Applied Probability. --- Distribution Theory. --- Probability Theory. --- Stochastic Modelling in Statistics. --- Actuarial Mathematics.

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This open access book discusses the statistical modeling of insurance problems, a process which comprises data collection, data analysis and statistical model building to forecast insured events that may happen in the future. It presents the mathematical foundations behind these fundamental statistical concepts and how they can be applied in daily actuarial practice. Statistical modeling has a wide range of applications, and, depending on the application, the theoretical aspects may be weighted differently: here the main focus is on prediction rather than explanation. Starting with a presentation of state-of-the-art actuarial models, such as generalized linear models, the book then dives into modern machine learning tools such as neural networks and text recognition to improve predictive modeling with complex features. Providing practitioners with detailed guidance on how to apply machine learning methods to real-world data sets, and how to interpret the results without losing sight of the mathematical assumptions on which these methods are based, the book can serve as a modern basis for an actuarial education syllabus.

Actuarial science. --- Statistics. --- Machine learning. --- Artificial intelligence—Data processing. --- Social sciences—Mathematics. --- Actuarial Mathematics. --- Statistics in Business, Management, Economics, Finance, Insurance. --- Machine Learning. --- Data Science. --- Mathematics in Business, Economics and Finance. --- Learning, Machine --- Artificial intelligence --- Machine theory --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Statistics --- Insurance --- Deep Learning --- Actuarial Modeling --- Pricing and Claims Reserving --- Artificial Neural Networks --- Regression Modeling --- Assegurances --- Estadística

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This text provides a comprehensive and detailed description of statistical methods for projecting mortality, and an extensive discussion of some important issues concerning the longevity risk in the area of life annuities and pension benefits.

Life insurance --- Mortality --- Assurance-vie --- Mathematics --- Mathématiques --- AA / International- internationaal --- 368.00 --- 368.3 --- 368.43 --- 307.13 --- 311.3 --- 10.03.d --- Theorieën over verzekeringen. Actuariële wetenschappen. --- Levensverzekering. --- Ouderdomsverzekering. Voorbarige dood. Weduwen en wezen. --- Statistieken van sterfte en sterftetabellen. --- Sterfte. Waarschijnlijke en gemiddelde levensduur. --- Actuariaat ; (Sterfte)tafels --- Mathématiques --- Life tables --- Mortality tables --- Mathematics. --- E-books --- Actuarial science --- Insurance --- Annuities --- BUSINESS & ECONOMICS --- Investments --- Pensions --- Assurance (Insurance) --- Coverage, Insurance --- Indemnity insurance --- Insurance coverage --- Insurance industry --- Insurance protection --- Mutual insurance --- Underwriting --- Finance --- Statistics --- Statistical models --- Insurance&delete& --- Risk Assessment & Management --- Theorieën over verzekeringen. Actuariële wetenschappen --- Levensverzekering --- Ouderdomsverzekering. Voorbarige dood. Weduwen en wezen --- Statistieken van sterfte en sterftetabellen --- Sterfte. Waarschijnlijke en gemiddelde levensduur --- Life insurance - Mathematics --- Mortality - Tables