Introduction to Ratemaking and Loss Reserving for Property and Casualty Insurance 3rd Edition

211 Pages·1986·13.69 MB·English

by  Robert L. Brown, Leon R. Gottlieb

Introduction to
Ratemaking and Loss Reserving
for Property and Casualty Insurance

Third Edition

Robert L. Browu
Ph.D., FSA, FCIA, ACAS
Leon R. Gottlieb
FCAS, MAAA

ACTEX Publications, Inc.
Winsted, Connecticut

Copyright © 2007, 2009 by ACTEX Publications, Inc.

All rights reserved. No portion of this book
may be reproduced in any fOIm or by any means
without the prior written permission of the
copyright owner.

Requests for permission should be addressed to:
ACTEX Publications
PO. Box 974
Winstcd, CT 06098

Manufactured in the United States ofAmerica

1098765432

Cover Design by Christine Phelps

Library of Congress Cataloging-in-Publication Data

Brown, Robert L., 1947-
lntroductiOn to ratemaking and loss reserving for
property and casualty insurance J Robert L. Brown,
Leon R. Gottlie. -- 3rd ed.

p. cm.
Includes index.
ISBN 978-1-56698-611-3 (pbk.
: alk. paper)
1. Insurance, Property"
Ratcs——United States. 2. Insurance, Casualty--Rates—-Unitcd States. 3.
lnsurance--Unitcd States—-Reserves.
I. Gottlieb, Leon R. [1. Title.

H08065.B?6 200?
368.1'01 10973-41022
2007002022

ISBN: 978-1-59968-611-3

iii

CONTENTS

Acknowledgements
Preface to First Edition
vii
Preface to Second Edition
ix
Preface to Third Edition
x

CHAPTER ONE - Why Insurance?
1

The Evolution of Insurance
I
How Insurance Works
3
insurance and Utility 6
What Makes a Risk Insurable
12
What Insurance 15 and 13 N01
[4
Risk, Peril, and Hazard
16
Purchase of Insurance: Other Reasons
16
Exercises
I?

bahbxinhnboixa;

CHAPTER TWO - Coverages
23

2.]
Introduction
23
2.2
Automobilelnsurance
24
2.2.1
Liabiiity Insurance (Section A)
26
2.2.2
Medical Benefits (Section B)
27
2.2.3
Uninsured and Under-
insured Motorist Coverage
27
2.2.4
Collision and
Other Than Collision (Section C)
28
2.3
Homeownerslnsurance
30
2.4
Tenants Package
3'?
2.5
Workers Compensation
38
2.6
FireInsurancc
4]
2.7
Marinelnsurance
42
2.8
Liabilitylnsurance
43
2.9
Limits to Coverage
44
2-9-1
Dcduclibles
44
2.9.2
Policy Limits 46
2.10 Conclusion
4?
2.11 Exercises 4?

iv

CHAPTER THREE - Ratemaking
51

3.1
Introduction
51
3.2
Objectives of Ratemaking
52
3.2.1
EsscnliaIObjectivcs
52
3.2.2
Non-Essenlial but Desirable Objectives
54
3.3
Frequency and Severity
55
3.4
Data for Raicmaking
56
3.4.1
AccidentYear
5?
3.4.2
PolicyYear
57
3.4.3
Calendachar
58
3.5
Premium Data
59
3.6
The Exposure Unit
59
3.7
The Expected Effective Period
60
3.8
Ingredients ofRatemaking
61
3.8.1
Loss-DevclopmentFactors
61
3.8.2
Trend Factors
64
3.8.3
Expenses
69
3.8.4
Loading for Profit and Contingencies
70
3.8.5
Credibility Factors
71
3.3.6
lnvestmcntincome
73
3.9
Rate Changes
?3
3.9.1
Overall Average Rate Change
?4
3.9.2 Changing Risk Classification Differentials
81
3.9.3
Baiancing Back
87
3.9.4 Summary ofthe Rate Change Procedure
89
3.10 Exercises
99

CHAPTER FOUR - Loss Reserving
111

4.1
Introduction
111
4.2
How Outstanding Claim Payments Arise
112
4.3
Definition ofTerms
114
4.3.l
Individual Claim File Estimates
114
4.3.2
GrossIBNR
115
4.3.3
Paid Loss Development
116
4.3.4
Incurred Loss Development
116
4.3.5
Saivagc and Subrogation
116
4.3.6
Loss AdjustmentExpenses
11?
4-3.7
FastTrack Reserves
ll'aT

4.4
ProfessionalConsiderations
11?
4.5
Checkingthe Data
119
4-6
Loss Reserving Methods
119
4.6.1
Case Reserves Plus
120
46.2
The Expected Loss Ratio Method
120
4.6-3
The Chain-Laddcr 0r
Loss-Dcvclopment Triangle Method
121
4.6.4
The Bomhuetter-Ferguson Method
133
4.6.5
Estimates Split into
Frequency and Severity
139
4.6.6
Summary
144
4.?
Discounting Loss Reserves
145
4.8
Exercises
149

CHAPTER FIVE - Intermediate Topics
159

5.1
Individual Risk Rating Plans
159
5.2
Increased Limits Factors
161
5.2.1
DataConsiderations
162
5.2.2
Loss Development
163
5.2.3
Trend
164
5.2.4
Risk
166
5.2.5
Expenses
[63
5.2.6
Loss Distributions
169
5.3
Reinsurance
1'10
5.3.1
Reserving for Reinsurance
176
5.4
Exercises
177

Appendix A
133
Answers to Text Exercises
187
Index
193

vii

ACKNOWLEDGEMENTS

The evolution of this textbook began with a set of class notes used to teach
an
introductory
properlyfcasualty
insurance
course
at
Univeristy
of
Waterloo. The original manuscript was prepared by Linda Lingard, and
reviewed by several groups of students and other instructors, most notably
Andrew R. Cartmell, FCAS. Their contributions to this project are greatly
appreciated.

In the course of developing the manuscript into textbook form, major
improvements were suggested by an industry review team comprised of
Susan M. 00220, FCAS, of Deloitte & Touche in Hartford, H. Elizabeth
Mitchell, FCAS, of English & American Insurance Corporation, David F.
Mohrmann, FCAS, of Tillinghastfl‘owers Perrin in Simsbury, and chaired
by
Susan
J.
Patschak,
FCAS,
also
of
the
Simsbury
office
of
Tillinghastfl‘owers
Perrin. A valuable review of the credibility theory
material was supplied by Dr. Thomas N. I-Ierzog, ASA.

The author especiaiiy appreciates the detaiied review of the manuscript,
as
to both content and
presentation, contributed by
Dr. Gerald
R.
Hartman, FCAS, of Temple University.

The text received final editorial and presentation polishing by the staff at
ACTEX Publications, including Marilyn J. Baleshiski, Sandi Lynn Fratini,
and Dick London, FSA.

The author expresses
his thanks and appreciation
to everyone who
contributed to the completion ofthis project.

ix

PREFACE T0 FIRST EDITION

The propertylcasuaity 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 propeltyfcasualty
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 pubiication has evoived out of a set of course notes that I have used
for nearly a decade to teach an introductory course in propertyi’casuaIty
insurance topics. The material can be ccwered comfombly in a tweive
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
propertylcasualty actuarial discipline. It is written from the perspective
of one who first qualified as a Feilow of the Society of Actuaries, and
then went on to achieve an Associateship in the Casualty Actuarial
Society, and to work extensively in the propertyfcasualty 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 calculus and probability theory,
including the concepts of random variables, density functions, expected

values, and variances. In addition, the mathematical topics of credibility,
regression analysis, continuous growth models, and compound interest make
brief appearances in the text.

Although the material presented here
is purely propenyieasualty
in
its
origins, the application of the knowledge gained
is much broader. The
methods
presented
here
have
potential
appiication
not
only
in
the
propertyfcasualty 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 propertylcasualty practice area, however. 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 Actuariai Society.

This publication is meant to whet the appetite for more. To that extent, I
invite you to partake and enjoy!

Waterloo, Ontario
Ruben L. Brown
March, I993

xi

PREFACE TO SECOND EDITION

I was delighted when
[ was asked to assist Rob Brown in updating this text.
The first edition has served the student community exceeding weil over the
past decade. It has provided a clear and insightful introduction to properly
casualty insurance and actuarial methods. While the book focuses on
ciassica! methods that have stood the test of time, it was appropriate 10 make
some changes to keep the book current. A brief overview of some mere
advanced applications of the basic principles has been added. Actuarial
practice continues to expand. Developments over the past decade include
risk based capital and dynamic financial analysis. In order to understand
these issues, knowledge of basic principles is needed.

I found contributing to a textbook, which requires keeping the student
reader always in mind, to be a challenging undertaking. This has given
me
an
even
greater
appreciation of Rob Brown’s
contribution
to
actuarial education. This book is not intended to be a substitute for the
syilabus 0f the Casualty Actuarial Society. it is designed to provide an
overview of core principles and methodologies, incorporating examples
as an educational tool. While we have attempted to keep actuarial jargon
to a minimum, it is important that the reader has a working knowledge of
certain insurance and actuarial terminology.

Rob and
I want to deeply thank Mary Hardy and Frank Bcnsics, FSA, for
their review and comments, and ACTEX editor Denise Roscngrant, for
her perseverance through the numerous drafts

March 2001
Leon R. Gottlieb, FCAS, MAAA
RobertL.Brown,Ph.D.,FSA,FC1A,ACAS

xii

PREFACE TO THIRD EDITION

Last August through a chance conversation with the President of ACTEX
publications, Gail Hall, we were informed that at the current mailing rate,
the Second Edition of our P&C textbook wOuId be out of stock by February
2007. Did we wish to write a Third Edition?

We took Gail up on this offer for a variety of reasons.

First, we knew it was important to keep the book content current. Al! points
of presentation have been updated.

Second, as Rob continued to use the textbook in the classroom, he had
written notes in his much«battered master copy of the book indicating
where the classroom presentation seemed superior to the existing textbook
material.

Third, Rob had continued to do some minor research in the area of P&C
Ratemaking and Loss Reserving and wanted to include some of this
expanded knowledge base into the textbook.

So, we agreed to write a Third Edition, which is now resting in your hands
or on your desk. The textbook was re-written on a day-to-day basis as Rob
taught the corresponding course at the University of Waterloo. We also had
several practicing aetuaries review the material and have included their
comments.

We think the Third Edition provides a measurable improvement in pedagogy
(even though we had thought the Second Edition was perfect when it
went to press in 2001).

Readers are reminded that this book is not intended to be a substitute for the
syllabus ofthe Casualty Actuarial Society. It is meant to be an Introduction to
the discipline, only.

xiii

We would like to thank the Following for their assistance in 1his endeavor:

Gail Hall, FSA, MAAA, President ofACTEX;
Marilyn Baleshiski, AC'I‘EX copy editor;

Scott Lennox, ASA, FCAS, FCIA Cooperators General of Canada; and

Joe] Kleinman, FCAS, Retired.

February, 2007"
Leon R. Gottlieb, FCAS, MAAA
Robert L. Brown, Ph.D., FSA, FCIA, ACAS

CHAPTER ONE

WHY INSURANCE?

1.] THE EVOLUTION OF INSURANCE

Humans have strived for security since the beginning of their existence. At

its earliest point, security existed ifthere was an assurance of food, warmth,
and shelter. The Bible relates the story of how, in ancient Egypt, Joseph set
aside part of the crop in good years in an attempt to cover the expected
shortfall in years Ofdrought‘

“The World Bank has recently identified casualty (or general)
insurance as a critical element for the development of emerging
economies.

This is only the latest recognition of the importance of casualty
insurance to economic development. The roots of insurance can be
traced back to Babyionia, over four thousand years ago, when
traders developed markets to insure the goods on their caravans
against loss on the hazardous trade routes. Without this form of
property insurance, traders would have been reluctant, or financially
unable, to engage in the trade that led to this nascent western
civilization.
Recognized as the oldest branch of insurance, marine
insurance was developed in ancient Greece and enabled trade to
occur
and
civilization
to
flourish.
Again,
forms
of casualty
insurance were the essential ingredients to economic development.
The lack of life insurance on the captain, or a pension system for the