Introduction to Ratemaking and Loss Reserving for Property and Casualty Insurance

212 Pages·2001·7.993 MB·English

by  Robert L. Brown, Leon R. Gottlieb

Introduction to
_ Ratemaking and Loss Reserving
for Property and Casualty Insurance
Second Edition
Robert L. Brown
|
Ph.D., FSA, FCIA, ACAS
piece eccece Leon R.G ottlieb
FCAS, MAAA

Introduction
to
Ratemaking and Loss Reserving
for
Property and Casualty
Insurance
Second Edition
Robert L. Brown, Ph.D., FSA, FCIA, ACAS
Leon R. Gottlieb, FCAS, MAAA
ACTEX Publications, Inc.
Winsted, Connecticut
Copyright © 2001, by ACTEX Publications, Inc.
All rights reserved. No portion of this book
may be reproduced in any form or by any means
without the prior written permission of the
copyright owner.
Requests for permission should be addressed to:
ACTEX Publications
P.O. Box 974
Winsted, CT 06098
Manufactured in the United States of America
10987654321
Cover Design by MUF
Library of Congress Cataloging-in-Publication Data
Brown, Robert L., 1949-
Introduction to ratemaking and loss reserving for property
and casualty insurance / Robert L. Brown.
p. cm.
Includes index.
ISBN 1-56698-394-0
1. Insurance, Property--United States--Rates and tables.
2. Insurance, Casualty--United States--Rates and tables.
3. Insurance--United States--Reserves. JI. Title.
HG8065.B76 1993
368.1'011'0973--dc20 93-20279
CIP
ISBN 1-59968-394-0
CONTENTS
Preface vii
Acknowledgements ix
Preface to Second Edition xi
CHAPTER ONE - Why Insurance?
1.1 The Evolution of Insurance 1
1.2 How Insurance Works 2
1.3. Insurance and Utility 3
1.4 What Makes a Risk Insurable 11
1.5 What Insurance Is and Is Not 13
1.6 Risk, Peril, and Hazard 14
1.7 Purchase of Insurance: Other Reasons 15
1.8 Exercises 16
CHAPTER TWO - Coverages
on Introduction 21
22 Automobile Insurance 21
2.2.1 Liability Insurance 22
2.2.2 Medical Benefits 23
2.2.3 Uninsured and Under
insured Motorist Coverage 25
2.2.4 Collision and Other Than Collision 26
23 Homeowners Insurance 28
2.4 Tenants Package 35
Z Workers Compensation 36
2.6 Fire Insurance 39
Dash Marine Insurance 40
2.8 Liability Insurance 41
2.9 Limits to Coverage 42
2.9.1 Deductibles 42
2.9.2 Policy Limits 44
2.10 Conclusion 45
2.11 Exercises 45
CHAPTER THREE - Ratemaking
ig) Introduction 49
3.2 Objectives of Ratemaking 50
3.2.1 Essential Objectives 50
3.2.2 Non-Essential but Desirable Objectives 52
a3 Frequency and Severity 53
3.4 Data for Ratemaking 54
3.4.1 Accident Year 55
3.4.2 Policy Year 55
3.4.3 Calendar Year 56
3,0 The Exposure Unit 57
3.6 The Expected Effective Period 58
2 Ingredients of Ratemaking 60
3.7.1 Loss-Development Factors 60
3.7.2 Trend Factors 62
3.7.3 Expenses 67
3.7.4 Loading for Profit and Contingencies 68
3.7.5 Credibility Factors 69
3.7.6 Investment Income 71
3.8 Rate Changes 72
3.8.1 Overall Average Rate Change 72
3.8.2 Changing Risk Classification Differentials 79
3.8.3 Balancing Back 85
3.8.4 Summary of the Rate Change Procedure 88
39 Exercises 96
CHAPTER FOUR - Loss Reserving
4.1 Introduction 109
4.2 How Outstanding Benefits Arise 110
4.3 Definition of Terms 112
4.3.1 Individual Claim File Estimates 112
4.3.2 Gross IBNR 113
4.3.3 Paid Loss Development 113
4.3.4 Incurred Loss Development 114
4.3.5 Salvage and Subrogation 114
4.3.6 Loss Adjustment Expenses 114
4.3.7 Fast Track Reserves 115
4.4 Professional Considerations 115
4.5 Checking the Data 117
4.6 Loss Reserving Methods 118
4.6.1 Case Reserves Plus 118
4.6.2 The Expected Loss Ratio Method 118
4.6.3 The Chain-Ladder or
Loss-Development Triangle Method 120
4.6.4 The Bornhuetter-Ferguson Method 132
vi
4.6.5 Estimates Split into
Frequency and Severity 136
4.6.6 Summary 140
4.7 Discounting Loss Reserves 141
4.8 Exercises 144
CHAPTER FIVE - Intermediate Topics
5.1 Individual Risk Rating Plans 151
5.2 Increased Limits Factors 153
5.2.1 Data Considerations 153
5.2.2 Loss Development 155
5.2.3 Trend 156
5.2.4 Risk 158
5.2, Selexpensesa15$
5.2.6 Loss Distributions 160
5.3 Reinsurance 161
5.3.1 Reserving for Reinsurance 167
5.4 Exercises 169
Appendix A 173
Answers to Text Exercises 177
Index 183
PREFACE
The property/casualty area is one of the fastest growing practice areas in
the actuarial profession. Because of this growth, there is a rapidly
growing demand for good pedagogical material in the property/casualty
discipline from university undergraduates, students in the early stages of
writing actuarial exams, and actuaries employed in other practice areas
who may have an interest in doing some property/ casualty work.
This publication has evolved out of a set of course notes that I
have used for nearly a decade to teach an introductory course in proper-
ty/casualty insurance topics. The material can be covered comfortably in
a twelve week teaching semester with time for review and problem
classes. The material also represents the basic foundation of knowledge
needed to gain an introductory appreciation of the building blocks of the
property/casualty actuarial discipline. It is written from the perspective
of one who first qualified as a Fellow of the Society of Actuaries, and
then went on to achieve an Associateship in the Casualty Actuarial
Society, and to work extensively in the property/casualty practice area in
Canada.
Very little background knowledge, either in mathematics or
insurance, is required for a reading of this text, with one important
exception. Section 1.3 on utility theory assumes a familiarity with calcu-
lus and probability theory, including the concepts of random variables,
density functions, expected values, and variances. In addition, the math-
ematical topics of credibility, regression analysis, continuous growth
models, and compound interest make brief appearances in the text.
viii
Although the material presented here is purely property/casualty
in its origins, the application of the knowledge gained is much broader.
The methods presented here have potential application not only in the
property/casualty practice area, but also in accident and sickness
insurance, group life and health insurance, and many other related areas.
Students of this introductory material should not presume to
have a working knowledge in the property/casualty practice area, how-
ever. To achieve that, the interested reader is advised and encouraged to
pursue the broader base of material available through the advanced
syllabus of the Casualty Actuarial Society.
This publication is meant to whet the appetite for more. To that
extent, I invite you to partake and enjoy!
Waterloo, Ontario Robert L. Brown
March, 1993