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From the reviews: "The huge literature in risk theory has been carefully selected and supplemented by personal contributions of the author, many of which appear here for the first time. The result is a systematic and very readable book, which takes into account the most recent developments of the field. It will be of great interest to the actuary as well as to the statistician . . ." -- Math. Reviews Vol. 43
Fundierte und anwendungsbezogene Einführung in die Wahrscheinlichkeitstheorie und Statistik. Ob digitale Nachrichtenübertragung, Schaltkreissimulation, Verfahrenstechnik oder Financial Engineering - die meisten modernen Verfahren in der Technik und Informatik beruhen auf stochastischen Prinzipien. Alle Resultate sind in diesem Buch ausführlich motiviert und exakt bewiesen. Hervorragend geeignet für Selbststudium und Vorlesungsbegleitung.
Die Arbeit diskutiert ein internes risikomaßbasiertes Modell zur Sicherheitskapitalbestimmung in der Schadenversicherung ("Solvency II") und beschäftigt sich am Beispiel risikoadjustierter Performancesteuerung mit der Frage, wie gesamtkollektive Sicherheitskapitalbedarfe risikogerecht auf untergeordnete Teileinheiten allokiert werden können. Koryciorz stellt die beiden zentralen Risikomaße Value-at-Risk und Conditional Value-at-Risk vor und untersucht sie hinsichtlich ihrer Güteeigenschaften. Bei der konkreten Sicherheitskapitalbestimmung liegt der modelltheoretische Schwerpunkt auf der Versicherungstechnik (Ausgleich im Kollektiv, Rückversicherung, Schadenabwicklung) und der adäquaten Erfassung stochastischer Abhängigkeiten. Neben einem Exkurs in die Extremwerttheorie findet darüber hinaus auch die Kapitalanlagetätigkeit der Versicherer Berücksichtigung. Zur Identifikation eines geeigneten Kapitalallokationsmechanismus formuliert der Autor intersubjektiv nachvollziehbare Gütekriterien (Axiomatik kohärenter Kapitalallokation), mittels derer die in der einschlägigen Literatur zur Anwendung kommenden Allokationsmethoden systematisch auf ihre Risikoadäquanz hin untersucht werden. Abschließend wird die Übertragung des EULER-Prinzips auf versicherungsspezifische Anwendungen kritisch beleuchtet.
Twenty-five years ago, Hans Blihlmann published his famous monograph Mathe matical Methods in Risk Theory in the series Grundlehren der Mathematischen Wis8enschaften and thus established nonlife actuarial mathematics as a recognized subject of probability theory and statistics with a glance towards economics. This book was my guide to the subject when I gave my first course on nonlife actuarial mathematics in Summer 1988, but at the same time I tried to incorporate into my lectures parts of the rapidly growing literature in this area which to a large extent was inspired by Blihlmann's book. The present book is entirely devoted to a single topic of risk theory: Its subject is the development in time of a fixed portfolio of risks. The book thus concentrates on the claim number process and its relatives, the claim arrival process, the aggregate claims process, the risk process, and the reserve process. Particular emphasis is laid on characterizations of various classes of claim number processes, which provide alternative criteria for model selection, and on their relation to the trinity of the binomial, Poisson, and negativebinomial distributions. Special attention is also paid to the mixed Poisson process, which is a useful model in many applications, to the problems of thinning, decomposition, and superposition of risk processe8, which are important with regard to reinsurance, and to the role of martingales, which occur in a natural way in canonical situations.
In the 1970's, the research agenda in insurance was dominatedby optimal insurance coverage, security design, and equilibrium underconditions of imperfect information. The 1980's saw a growth oftheoretical developments including non-expected utility, pricevolatility, retention capacity, the pricing and design of insurancecontracts in the presence of multiple risks, and the liabilityinsurance crisis. The empirical study of information problems, financial derivatives, and large losses due to catastrophic eventsdominated the research agenda in the 1990's.The "Handbook of Insurance" provides a single reference source oninsurance for professors, researchers, graduate students, regulators, consultants, and practitioners, that reviews the research developmentsin insurance and its related fields that have occurred over the lastthirty years. The book starts with the history and foundations ofinsurance theory and moves on to review asymmetric information, riskmanagement and insurance pricing, and the industrial organization ofinsurance markets. The book ends with life insurance, pensions, andeconomic security.Each chapter has been written by a leading authority in insurance, allcontributions have been peer reviewed, and each chapter can be readindependently of the others.

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