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This book offers a mathematical introduction to non-life insurance and, at the same time, to a multitude of applied stochastic processes. It gives detailed discussions of the fundamental models for claim sizes, claim arrivals, the total claim amount, and their probabilistic properties. Throughout the book the language of stochastic processes is used for describing the dynamics of an insurance portfolio in claim size space and time. In addition to the standard actuarial notions, the reader learns about the basic models of modern non-life insurance mathematics: the Poisson, compound Poisson and renewal processes in collective risk theory and heterogeneity and Bühlmann models in experience rating. The reader gets to know how the underlying probabilistic structures allow one to determine premiums in a portfolio or in an individual policy. Special emphasis is given to the phenomena which are caused by large claims in these models. What makes this book special are more than 100 figures and tables illustrating and visualizing the theory. Every section ends with extensive exercises. They are an integral part of this course since they support the access to the theory. The book can serve either as a text for an undergraduate/graduate course on non-life insurance mathematics or applied stochastic processes. Its content is in agreement with the European "Groupe Consultatif" standards. An extensive bibliography, annotated by various comments sections with references to more advanced relevant literature, make the book broadly and easiliy accessible.
Insurance --- Stochastic processes. --- Mathematics. --- -Stochastic processes --- 368.00151962 --- Random processes --- Probabilities --- Assurance (Insurance) --- Coverage, Insurance --- Indemnity insurance --- Insurance coverage --- Insurance industry --- Insurance protection --- Mutual insurance --- Underwriting --- Finance --- Mathematics --- Stochastic processes --- Assurance --- Processus stochastiques --- Mathématiques --- Economics, Mathematical . --- Quantitative Finance. --- Economics --- Mathematical economics --- Econometrics --- Methodology
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519.216 --- Stochastic analysis --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- 519.216 Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Stochastic processes in general. Prediction theory. Stopping times. Martingales --- 303.3 --- AA / International- internationaal --- 519.218 --- 519.218 Special stochastic processes --- Special stochastic processes --- Waarschijnlijkheid. Probabiliteit. Nauwkeurigheid. Residuals: measurement and specification (wiskundige statistiek) --- Actuarial mathematics --- Stochastic analysis. --- Analyse stochastique --- Probabilités
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Actuarial mathematics --- Insurance --- Poisson processes --- 368.00 --- 51 --- AA / International- internationaal --- 368 --- 368 Verzekeringswezen --- Verzekeringswezen --- Processes, Poisson --- Point processes --- Business mathematics --- Actuarial science --- Mathematics --- Theorieën over verzekeringen. Actuariële wetenschappen --- Wiskunde
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Both in insurance and in finance applications, questions involving extremal events (such as large insurance claims, large fluctuations in financial data, stock market shocks, risk management, ...) play an increasingly important role. This book sets out to bridge the gap between the existing theory and practical applications both from a probabilistic as well as from a statistical point of view. Whatever new theory is presented is always motivated by relevant real-life examples. The numerous illustrations and examples, and the extensive bibliography make this book an ideal reference text for students, teachers and users in the industry of extremal event methodology.
Business mathematics. --- Insurance --- Mathematics. --- Business mathematics --- Insurance - Mathematics --- 332.015195 --- Mathematical models --- 10.03.a --- 305.6 --- AA / International- internationaal --- 330.105 --- Actuarial science --- 330.105 Wiskundige economie. Wiskundige methoden in de economie --- Wiskundige economie. Wiskundige methoden in de economie --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Finance --- Mathematics --- Actuariaat ; Algemeen --- Risicotheorie, speltheorie. Risicokapitaal. Beslissingsmodellen --- Mathematical statistics --- Probabilités --- Statistique --- Mathématiques financières --- Assurance --- Mathématiques
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