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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

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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.  .

Quantitative methods (economics) --- Finance --- Economics --- Operational research. Game theory --- Mathematical statistics --- Probability theory --- Mathematics --- Financial analysis --- Planning (firm) --- Business economics --- financieel management --- toegepaste wiskunde --- waarschijnlijkheidstheorie --- stochastische analyse --- economie --- mathematische modellen --- statistiek --- financiële analyse --- econometrie --- wiskunde --- operationeel onderzoek --- kansrekening

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Dieses Lehrbuch bietet eine umfassende, moderne Einführung in die wesentlichen Themen und Anwendungen der Wahrscheinlichkeitstheorie. Es liefert eine sehr gut motivierte, anspruchsvolle und weitreichende Darstellung, bleibt aber dennoch vorlesungsnah und verzichtet auf unnötige formalistische Hürden. Ziel des Autors ist es insbesondere, die Bedeutung und Faszination dieses Gebiets für zentrale Anwendungen spürbar werden zu lassen. Das Buch ermöglicht dem Leser somit, ein hervorragendes Verständnis der Begriffe, Methoden und der Kerninhalte der Wahrscheinlichkeitstheorie sowie der Grundlagen der stochastischen Prozesse und deren Anwendungen zu gewinnen. .

Probabilities. --- Probability Theory and Stochastic Processes.

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"The first systematic treatment of model risk, this book provides the tools needed to quantify and assess the impact of model uncertainty. It will be essential for all those working in portfolio theory and the theory of financial and engineering risk, for practitioners in these areas, and for graduate courses on risk bounds and model uncertainty"--

Risk management. --- Management. --- Computer simulation. --- International finance --- International financial management --- Operational research. Game theory

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Marginal distributions --- Congresses