Bonus-Malus Systems in Automobile Insurance
Most insurers around the world have introduced some form of merit-rating in automobile third party liability insurance. Such systems, penalizing at-fault accidents by premium surcharges and rewarding claim-free years by discounts, are called bonus-malus s
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Huebner International Series on Risk, Insurance, and Economic Security J. David Cummins, Editor The Wharton School University of Pennsylvania Philadelphia, Pennsylvania, USA Series Advisors: Dr. Phelim P. Boyle University of Waterloo, Canada Dr. Jean Lemaire University of Pennsylvania, USA Professor Akihiko Tsuboi Kagawa University, Japan Dr. Richard Zeckhauser Harvard University, USA
Other books in the series: Cummins, J. David and Derrig, Richard A.: Classical
Insurance Solvency Theory
Borba, Philip S. and Appel, David: Benefits, Costs, and
Cycles in Workers' Compensation Cummins, J. David and Derrig, Richard A.: Financial Models
of Insurance Solvency Williams, C. Arthur: An International Comparison of
Workers' Compensation Cummins, J. David and Derrig, Richard A.: Managing the
Insolvency Risk of Insurance Companies Dionne, Georges: Contributions to Insurance Economics Dionne, Georges and Harrington, Scott E.: Foundations of
Insurance Economics
Klugman, Stuart A.: Bayesian Statistics in Actuarial Science Durbin, David and Borba, Philip: Workers' Compensation Insurance:
Claim Costs, Prices and Regulation Cummins, J. David: Financial Management of Life Insurance
Companies Gustavson, Sandra G. and Harrington, Scott E.: Insurance,
Risk Management, and Public Policy
BONUS-MALUS SYSTEMS IN AUTOMOBILE INSURANCE
by Jean Lemaire of The Wharton School at The University of Pennsylvania
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Springer Science+13usiness Media, LLC
Library of Congress Cataloging~in-Publication Data Bonus-malus systems in aUiomobile insurance 1 [Jean Lemaire, editor). p . cm. -- (Huebner international series on risk, insurance and economic security : 19) Includes bibliographical references and index. ISBN 978-94-011-0631-3 (eBook) ISBN 978-94-010-42758 DOI 10.1007/978-94-011-0631-3 I. Insurance , Automobile--Rates and tables. I. Lemaire, Jean. II. Series HG9970.2.B66 1995 368'.092--dc20 94-41825 CIP
Copyright It' 1995 by Springer Sciencc+Business Media New York Originally published by Kluwer Academic Publishers in 1995 Softcover reprint of the hardcover Ist edition 1995 All rights reserved . No pan of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical , photo-copying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, LLC .
Primed on acid-free paper.
Contents
List of Figures
ix
List of Tables
xi
Preface
xv
Main Notations
xxv
Part 1 Introduction: Models for Claim Number Distributions
Introduction: Definition of a Bonus-Malus System
3
2 A Typical Bonus-Malus Evolution: The Belgian Case
11
3 Models for the Claim Number Distribution
21
Appendix A Applications in Other Disciplines
43
Part 2 Evaluation of Bonus-Malus Systems
57
4
Tool I: The Relative Stationary Average Level
59
VI
CONTENTS
5 Tool 2: The Coefficient of Variation of the Insured's Premiums
67
6 Tool 3: The Elasticity of the Bonus-Malus System
71
7 Tool 4: The Average Optimal Retention
91
8 An Index of
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