Modern Actuarial Risk Theory
Apart from standard actuarial theory, Modern Actuarial Risk Theory contains methods that are relevant for actuarial practice, for instance the rating of automobile insurance policies, premium principles and IBNR models, as well as generalized linear model
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Modern Actuarial Risk Theory by
Rob Kaas University of Amsterdam, The Netherlands
Marc Goovaerts Catholic University of Leuven, Belgium and University of Amsterdam, The Netherlands
Jan Dhaene Catholic University of Leuven, Belgium and University of Amsterdam, The Netherlands
and
Michel Denuit Université Catholique de Louvain, Belgium
KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW
eBook ISBN: Print ISBN:
0-306-47603-7 0-7923-7636-6
©2002 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2001 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's eBookstore at:
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Foreword Risk Theory has been identified and recognized as an important part of actuarial education; this is for example documented by the Syllabus of the Society of Actuaries and by the recommendations of the Groupe Consultatif. Hence it is desirable to have a diversity of textbooks in this area. I welcome the arrival of this new text in risk theory, which is original in several respects. In the language of figure skating or gymnastics, the text has two parts, the compulsory part and the free-style part. The compulsory part includes Chapters 1–4, which are compatible with official material of the Society of Actuaries. This feature makes the text also useful to students who prepare themselves for the actuarial exams. Other chapters are more of a free-style nature, for example Chapter 10 (Ordering of Risks, a speciality of the authors). And I would like to mention Chapter 8 in particular: to my knowledge, this is the first text in risk theory with an introduction to Generalized Linear Models. Special pedagogical efforts have been made throughout the book. The clear language and the numerous exercises are an example for this. Thus the book can be highly recommended as a textbook. I congratulate the authors to their text, and I would like to thank them also in the name of students and teachers that they undertook the effort to translate their text into English. I am sure that the text will be successfully used in many classrooms. H.U. Gerber
Lausanne, October 3, 2001
v
Preface This book gives a comprehensive survey of non-life insurance mathematics. It was originally written for use with the actuarial science programs at the Universities of Amsterdam and Leuven, but its Dutch version has been used at several other universities, as well as by the Dutch Actuarial Society. It provides a link to the further theoretical study of actuarial science. The methods presented can not only be used in non-life insurance, but are also effective in other branches of actuarial science, as well as, of course, in actuarial practice. Apart from the standard theory, this text contains methods that are directly
