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Non-Life Insurance Mathematics
An Introduction with the Poisson Process
Taschenbuch von Thomas Mikosch
Sprache: Englisch

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Beschreibung
The second edition of this book contains both basic and more advanced - terial on non-life insurance mathematics. Parts I and II of the book cover the basic course of the 1rst edition; this text has changed very little. It aims at the undergraduate (bachelor) actuarial student as a 1rst introduction to the topics of non-life insurance mathematics. Parts III and IV are new. They can serve as an independent course on stochastic models of non-life insurance mathematics at the graduate (master) level. The basic themes in all parts of this book are point process theory, the Poisson and compound Poisson processes. Point processes constitute an - portant part of modern stochastic process theory. They are well understood models and have applications in a wide range of applied probability areas such as stochastic geometry, extreme value theory, queuing and large computer networks, insurance and finance. The main idea behind a point process is counting. Counting is bread and butter in non-life insurance: the modeling of claim numbers is one of the - jor tasks of the actuary. Part I of this book extensively deals with counting processes on the real line, such as the Poisson, renewal and mixed Poisson processes. These processes can be studied in the point process framework as well, but such an approach requires more advanced theoretical tools.
The second edition of this book contains both basic and more advanced - terial on non-life insurance mathematics. Parts I and II of the book cover the basic course of the 1rst edition; this text has changed very little. It aims at the undergraduate (bachelor) actuarial student as a 1rst introduction to the topics of non-life insurance mathematics. Parts III and IV are new. They can serve as an independent course on stochastic models of non-life insurance mathematics at the graduate (master) level. The basic themes in all parts of this book are point process theory, the Poisson and compound Poisson processes. Point processes constitute an - portant part of modern stochastic process theory. They are well understood models and have applications in a wide range of applied probability areas such as stochastic geometry, extreme value theory, queuing and large computer networks, insurance and finance. The main idea behind a point process is counting. Counting is bread and butter in non-life insurance: the modeling of claim numbers is one of the - jor tasks of the actuary. Part I of this book extensively deals with counting processes on the real line, such as the Poisson, renewal and mixed Poisson processes. These processes can be studied in the point process framework as well, but such an approach requires more advanced theoretical tools.
Über den Autor

Thomas Mikosch has been professor at the Laboratory of Actuarial Mathematics of the University of Copenhagen since January 2001. Before this, he held positions in Dresden (Germany), Wellington (New Zealand) and Groningen (Netherlands). His special interests are applied probability theory and stochastic processes. Over the last few years his research has focused on extremal events in finance, insurance and telecommunications. His earlier very successful book, written jointly with Paul Embrechts and Claudia Klüppelberg, Modelling Extremal Events for Finance and Insurance (1997), is also published by Springer.

Zusammenfassung

A mathematicalintroduction 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. What makes this book special are more than 100 figures and tables illustrating and visualizing the theory. Every section ends with extensive exercises. The book can serve either as a text for an undergraduate/graduate course on non-life insurance mathematics or applied stochastic processes.

Inhaltsverzeichnis
Collective Risk Models.- The Basic Model.- Models for the Claim Number Process.- The Total Claim Amount.- Ruin Theory.- Experience Rating.- Bayes Estimation.- Linear Bayes Estimation.- A Point Process Approach to Collective Risk Theory.- The General Poisson Process.- Poisson Random Measures in Collective Risk Theory.- Weak Convergence of Point Processes.- Special Topics.- An Excursion to L#x00E9;vy Processes.- Cluster Point Processes.
Details
Erscheinungsjahr: 2009
Fachbereich: Wirtschaftsratgeber
Genre: Wirtschaft
Rubrik: Recht & Wirtschaft
Medium: Taschenbuch
Reihe: Universitext
Inhalt: xv
432 S.
55 s/w Illustr.
432 p. 55 illus.
ISBN-13: 9783540882329
ISBN-10: 3540882324
Sprache: Englisch
Herstellernummer: 12524501
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Mikosch, Thomas
Auflage: 2nd ed. 2009
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Universitext
Maße: 235 x 155 x 25 mm
Von/Mit: Thomas Mikosch
Erscheinungsdatum: 25.03.2009
Gewicht: 0,674 kg
Artikel-ID: 101718350
Über den Autor

Thomas Mikosch has been professor at the Laboratory of Actuarial Mathematics of the University of Copenhagen since January 2001. Before this, he held positions in Dresden (Germany), Wellington (New Zealand) and Groningen (Netherlands). His special interests are applied probability theory and stochastic processes. Over the last few years his research has focused on extremal events in finance, insurance and telecommunications. His earlier very successful book, written jointly with Paul Embrechts and Claudia Klüppelberg, Modelling Extremal Events for Finance and Insurance (1997), is also published by Springer.

Zusammenfassung

A mathematicalintroduction 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. What makes this book special are more than 100 figures and tables illustrating and visualizing the theory. Every section ends with extensive exercises. The book can serve either as a text for an undergraduate/graduate course on non-life insurance mathematics or applied stochastic processes.

Inhaltsverzeichnis
Collective Risk Models.- The Basic Model.- Models for the Claim Number Process.- The Total Claim Amount.- Ruin Theory.- Experience Rating.- Bayes Estimation.- Linear Bayes Estimation.- A Point Process Approach to Collective Risk Theory.- The General Poisson Process.- Poisson Random Measures in Collective Risk Theory.- Weak Convergence of Point Processes.- Special Topics.- An Excursion to L#x00E9;vy Processes.- Cluster Point Processes.
Details
Erscheinungsjahr: 2009
Fachbereich: Wirtschaftsratgeber
Genre: Wirtschaft
Rubrik: Recht & Wirtschaft
Medium: Taschenbuch
Reihe: Universitext
Inhalt: xv
432 S.
55 s/w Illustr.
432 p. 55 illus.
ISBN-13: 9783540882329
ISBN-10: 3540882324
Sprache: Englisch
Herstellernummer: 12524501
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Mikosch, Thomas
Auflage: 2nd ed. 2009
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Universitext
Maße: 235 x 155 x 25 mm
Von/Mit: Thomas Mikosch
Erscheinungsdatum: 25.03.2009
Gewicht: 0,674 kg
Artikel-ID: 101718350
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