Non-Life Insurance Mathematics An Introduction with the Poisson Proc
The volume offers a mathematical introduction to non-life insurance and, at the same time, to a multitude of applied stochastic processes. It includes detailed discussions of the fundamental models regarding claim sizes, claim arrivals, the total claim am
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Non-Life Insurance Mathematics An Introduction with the Poisson Process Second Edition
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Thomas Mikosch Department of Mathematical Sciences University of Copenhagen Universitetsparken 5 2100 Copenhagen Denmark [email protected]
ISBN 978-3-540-88232-9
e-ISBN 978-3-540-88233-6
DOI 10.1007/978-3-540-88233-6 Library of Congress Control Number: 2008943236 Mathematics Subject Classification (2000): 91B30, 60G35, 60K10 c Springer-Verlag Berlin Heidelberg 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper springer.com
Preface to the Second Edition
The second edition of this book contains both basic and more advanced material on non-life insurance mathematics. Parts I and II of the book cover the basic course of the first edition; this text has changed very little. It aims at the undergraduate (bachelor) actuarial student as a first 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 important 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 major 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. Parts I and II of this text are kept at a level which requires basic knowledge of probability theory and stochastic processes. Such knowledge is typically available in the 2nd or 3rd year of a bachelor program with a mathematical, statistical, actuarial or econometric orientation. The n
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