Modern Actuarial Theory and Practice, Second Edition

809 Pages·2004·12.69 MB·English

by  Philip Booth

Modern Actuarial
Theory and
Practice
Second Edition
© 2005 by Taylor & Francis Group, LLC
Modern Actuarial
Theory and
Practice
Second Edition
Philip Booth
Cass Business School, City University, London
Robert Chadburn
BPP Actuarial Education, Abingdon, Oxon
Steven Haberman
Cass Business School, City University, London
Dewi James
James Brennan & Associates, London
Zaki Khorasanee
Cass Business School, City University, London
Robert H. Plumb
Cass Business School, City University, London
Ben Rickayzen
Cass Business School, City University, London
CHAPMAN & HALL/CRC
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Foreword
The publication of the first edition of Modern Actuarial Theory and Practice
in 1998 marked an important step in the emergence of new actuarial
textbooksintheEnglishlanguage.Althoughtherehadbeenmanyadvances
inthetheoryandpracticalapplicationofactuarialscience,andconsiderable
development in thinking about the way in which the subject should
be presented and taught, there had been relatively few new actuarial
textbooks. A decade or so ago the U.K. actuarial profession (the Faculty of
Actuaries and the Institute of Actuaries) stopped relying on textbooks for
educating new generations of actuaries and began to develop its own
corereadingaroundthedefinedsyllabusobjectives,relyingoncommercial
tuition providers and the universities to develop more tailored tuition
materials to assist students in preparing for the examinations.
Nevertheless, there remained (and remains) a great need for textbooks,
inparticulartosupporttheteachingofactuarialscienceintheuniversities,
where there have been an increasing number of first-degree and post-
graduate diploma programs in the fields of actuarial science and financial
mathematics. It is also important for the actuarial profession to ensurethat
the fundamentals of actuarial science and its applications are accessible,
both to current and future generations of actuaries, in permanent and
codified form, through the availability of high-quality textbooks.
Thereisagrowingneedfortextbookstosupporttheinternationalization
of actuarial education, in particular to cover the application of actuarial
principles and techniques in the major practice areas of the profession.
The International Actuarial Association (IAA) insists that all member
associations should have in place by 2005 an actuarial education process
that satisfies the requirements of the IAA Core Syllabus and Guidelines,
which the IAA adopted in 1998. Two key elements of the Core Syllabus
are the subjects Investment and Asset Management and Principles of Actuarial
Management, which form the subject matter of Modern Actuarial Theory
and Practice.
MutualrecognitionofprofessionalqualificationswithintheE.U.isalready
a fait accompli, following the passing of the Higher Education Diplomas
Directive in 1988. The actuarial profession has embraced this concept
actively, with mutual admission to professional bodies and a determined
v
© 2005 by Taylor & Francis Group, LLC
vi Foreword
effort to harmonize the qualifications of actuaries throughout the E.U.
Like the IAA, the European Actuarial Consultative Group (the Groupe
Consultatif) has approved a core syllabus for the education of a fully
professional actuary, which all member associations are expected to have
implementedinfullby2005,incooperationwithotherrelevantinstitutions,
including the universities, which in many countries play a dominant role
in the actuarial education process. The core syllabus is annotated with
references to suitable textbooks to cover the various topics. Prominent
amongthesereferences—forseveralofthesubjectsinthecoresyllabus—is
Modern Actuarial Theory and Practice.
Internationally, there are many good textbooks addressing the
fundamental mathematics of actuarial science and associated disciplines.
However, there is relatively little teaching material dealing with the prac-
tical and professional applications of actuarial science. Modern Actuarial
Theory and Practice has helped to fill that gap, providing an introduction
to the practical applications of modern developments in actuarial science
across a range of practice areas. The material is presented, to the greatest
extent possible, in generic terms, so that it will be accessible and useful to
an international audience.
In the years since the publication of the first edition there has been
considerable development of thinking in the actuarial profession to incor-
porate ideas and theories from the rapidly growing field of financial
economics. Market-consistent valuation methods have taken center stage
and the International Accounting Standards Board is working towards
theintroductionofInternationalFinancialReportingStandardsforpension
funds, insurance companies, banks and other financial institutions that
will be based on fair value of assets and liabilities. The authors have
updated the first edition to reflect these developments and have also
introduced a new section of the book on actuarial applications in the fields
of health and long-term care. The pensions section is also now more
balanced between defined benefit (DB) and defined contribution (DC)

arrangements, reflecting the trend in the UK and in many other countries
away from DB and towards DC.
TheneweditionofModernActuarialTheoryandPracticewilloffervaluable
additional study material for those preparing for the Core Applications
examinations of the U.K. actuarial profession, and similar-level studies in
other countries, as well as being a convenient general textbook for every
qualified actuary to have on their bookshelf.
Icongratulatetheauthorsonbringingthematerialtogetherforthisbook,
andhopethatitwillbewidelyusedbystudentsandbyqualifiedactuaries
around the world.
Chris Daykin CB, MA, FIA
Chairman, Education Committee of the Groupe Consultatif
© 2005 by Taylor & Francis Group, LLC
Introduction
Thisbookisspecificallyaimedatfinal-yearundergraduates,M.Sc.students,
research students preparing for an M.Phil. or Ph.D. degree, and student
actuaries preparing for the actuarial examinations of various professional
bodies. Practising actuaries may also find the book a useful guide to
current thinking, methodologies, and models. Although all of the authors
are U.K.-based, the book has been written with the intention of presenting
the principles of actuarial science (rather than the details of practices
specific to certain jurisdictions). Thus, various illustrative examples have
been taken from the U.K. and the U.S.
The book describes the traditional areas of actuarial activity, but in
a manner which highlights the fundamental principles of actuarial theory
and practice, as well as their economic, financial, and statistical founda-
tions. The commonalities and synergies between the different practice
areas are emphasized. The last 25years have seen a significant shift in
thinking and in approach—from deterministic methods, with implicit
or explicit margins to protect against variability, to stochastic methods and
a full recognition of the nature of risk. This shift is reflected in the
presentation of the material in this book.
The second edition updates the first edition with changes in actuarial
thinking, technique, and application over the last 5years. Specific changes
relate to Part IV, on Pensions, which has been extended to provide a
balanced treatment of defined-benefit and defined-contribution pension
plans. Also, a new part has been added to reflect the growing significance
ofactuarialapplicationsinthefieldsofdisability,health,andlong-termcare
insurance.
At the time of publication, changes in actuarial education are being
implemented in several countries. As Chris Daykin mentions in his
Foreword, both the International Actuarial Association and the European
Actuarial Consultative Group have approved core syllabuses which
member associations are expected to have fully implemented by 2005.
Ithasbeen one ofourobjectivestoensurethat thecontentandstructureof
the book match the philosophy of these developments on the international
front, as well as the manner in which actuarial qualifications are changing
and are likely to change in the future.
vii
© 2005 by Taylor & Francis Group, LLC
viii Introduction
The detailed structure of the book is as follows.
Part I, Investment, comprises Chapter 1 to Chapter 5. Most actuaries are
employed by intermediary companies working in the financial services
sector. These companies have both financial assets and financial liabilities.
A crucial part of the role of the actuary is the management of asset liabil-
ity risk, which involves both the management of investments and the
joint management of assets and liabilities. Although the book takes an
‘‘institutional’’ approach, Chapter 1 stands out in giving an overview of
financial intermediaries and their economic functions and in looking at
how they might evolve over time. In doing this, the chapter brings out
the similarities and differences between the institutions discussed in detail
in the later chapters and points out that the techniques and method-
ologiesusedbyonetypeofinstitutioncouldbeexportedtoothertypesthat
perform the same kind of economic function.
Chapter 2 looks at the investments available to financial institutions.
Each of the main types of investment is analyzed from economic and risk
perspectives.Techniquesofvaluationarediscussed.Thosewhoarefamiliar
with the principles of investment can omit this chapter without loss of
continuity.
Chapter 3 examines the principles of asset liability management and
the management of investment risk from a conceptual viewpoint. It then
applies these ideas to different types of financial institution and compares
and contrasts the investment policy of these different types of institu-
tion. International differences are also discussed and rationalized in terms
of the principles presented earlier in the chapter.
Chapter4developsanumberofdifferentapproachestothemeasurement
of investment risk, including utility theory, coherent risk measures, and
the use of shortfall constraints. The discussion also considers the critical
conceptual (and practical) trade-off between risk and return.
Chapter5buildsonthediscussioninChapter4.Actuarialscienceisoften

described as a mixture of judgement and application of scientific tech-
niques. Chapter 5 discusses some of the scientific techniques that are used
to determine investment policy in terms of portfolio selection and asset
allocation. Investment problems can be so complex that simulation and
numerical methods are more useful than analytical techniques. Chapter 5
goes on to discuss the subject of stochastic investment modeling and
considers its application to asset allocation within a financial institution,
in the presence of liabilities.
Followingonfromthisgeneralanalysisofthemanagementofassets,Part
II, Life Insurance, considers actuarial management in respect of the major
types of liability structure, describing the process of financial intermedia-
tion through life insurance and other long-term insurance-based contracts.
The basic operation and general nature of life insurance are described
in Chapter 6. The aim is to give a brief description of the types of product
© 2005 by Taylor & Francis Group, LLC
Introduction ix
available and how they are distributed, with particular examples from
the U.S. and the U.K. The chapter also introduces the nature of the risks
faced by life insurers, as a preface to the more detailed discussions in
Chapter 10 and Chapter 11.
Chapter7andChapter8aredevotedtotheoperationofnonparticipating
and participating long-term insurance contracts, again with reference to
the U.S. and the U.K. Chapter 8 examines the different profit distribu-
tion methods that are in common use inernationally, i.e., the contribution
method, the uniform reversionary bonus method, revalorization methods,
and the accumulating with profits method. Simplenumericalexamples are
given in order to illustrate the financial operation of these benefit struc-
tures.Thetwochaptersincludeafulldiscussionofapproachestoreserving
and their financial effects. Chapter 9 describes the process and rationale
for the solvency regulation of long-term insurance business, using the E.U.
approach as an example. The significant financial effects of such regula-
tion on the reserves of life insurers and, hence, upon profit emergence are
discussedforthemaintypesofcontract.Again,simplenumericalexamples
are given.
Havingbuiltupasoundunderstandingofthefinancialoperationofalife
insurance business, the reader confronts the financial risks carried by life
insurers.Chapter10discussesthevariousmethodsandtechniquesthatare
available to control such risks, including underwriting and reinsurance.
Chapter 11 discusses the role of the actuary in the control of life insur-
ance company risks, based on the concept of the ‘‘control cycle’’. Product
pricing is also discussed. The use of appropriate modeling techniques
is promoted as an aid to the actuary in preparing his or her advice. In
particular, whole-office modeling techniques are thoroughly described.
Both stochastic and deterministic approaches are considered, and the
chapter concludes with warnings regarding the risks that may arise from
modeling errors.
Part III, General Insurance, comprises Chapter 12 to Chapter 16. The aim

is to demonstrate ways in which the profitability of general insurance
companies and the security of the policyholders can besafeguardedby the
application of scientific procedures for the classification and assessment
ofrisksandtheestablishmentofadequatepremiumbasesandreserves.The
focus is on the practical aspects of understanding the underlying pro-
cesses.Therangeofperilstowhichgeneralinsurancecontractsareexposed
is much broader than a typical life insurance contract. The general
insurance market aims to indemnify policyholders in the event of loss or
injury due to a wide range of perils. The scope of general insurance
policies and the variety of clients mean that, frequently, the data required
to measure pricing and profitability are limited. This leads to significantly
greater parameter estimation error in general insurance actuarial models
thanisthecasewithlifeinsurance.Carefulpolicydesignandmanagement
can help to control some of the uncertainty, and retrospective premium
© 2005 by Taylor & Francis Group, LLC
x Introduction
rating (or profit sharing) provides a means of absorbing the problem of
estimation error.
Inmostfreemarketsthepriceachievedforagivenriskismoreafunction
of the supply and demand of insurance capacity than of a theoretically
ideal level. The insurance market is no exception. Swings in market
prices,arisinginteraliafromamismatchbetweensupplyanddemand,are
a fundamental feature of general insurance.
Chapter 12 provides an introduction to general insurance markets
and contracts. In order to gain an appreciation of the dynamics of a
general insurance company’s operations, readers will need an under-
standing of the underlying accounting framework, and this is introduced
in Chapter 13.
Chapter 14 emphasizes the importance of understanding the ‘‘true’’
underlying risk premium. It then examines the reasons for differences
between that and the premium charged in order to understand the contri-
bution of each class of business to the overall profitability of the insurer.
For commercial insurers, the reinsurance market provides access to
additional capital and assistance with the development of products for
new and unusual risks. Chapter 15 discusses some of the ways in which
this market operates. Reinsurance is a swiftly changing area of opera-
tion. Brokers and insurers develop products with characteristics similar to
derivatives in order to compete with other financial institutions, such as
banks, which are designing insurance-type products and offering hedging
opportunities. The chapter closes with consideration of such alternative
methods of risk transfer.
Chapter16setsouttheprocessesthatleadtoaclaimentryonaninsurer’s
books.Itdescribessomebasicmethodswhichmaybeappliedinprojecting
claims to an ultimate level and, hence, in the estimation of claims reserves.
The availability of increased computing power and developments in
statistical modeling have led to a proliferation of regression techniques
for modeling the behavior of the claims run-off triangle. Some of these are

discussed briefly.
Chapter 17 to Chapter 20 constitute Part IV, Pensions, and they provide a
general introduction to the subject of pension provision.
The extent and type of private-sector pension provision in developed
countries appears to be driven by two main factors. First, those countries
with state schemes providing a high level of replacement income, such as
Germany, tend to have less-developed private provision; those with a low
levelofstatebenefit,suchastheU.S.,havewell-developedsectors.Second,
countries which give tax advantages to certain types of pension plan are
more likely to have this type of provision.
Nonetheless,certainmajorcharacteristicsarefoundinmostsystems,and
these are highlighted in the coverage here. They include: aspects of benefit
design,suchastheprovisionofretirementincomeanddependants’benefits
in defined-benefit pension plans; the types of financing in prefunded
© 2005 by Taylor & Francis Group, LLC
Introduction xi
pension plans; the nature of actuarial modeling; and the general principles
of investment to meet the future liabilities of pension plan members.
Chapter 17 provides an overview of pension plans, describing the main
features of defined-benefit, defined-contribution, and hybrid plans. For
prefunded defined-benefit plans, actuarial modeling plays a role of critical
importanceinthedeterminationoflevelsoffundingandintheassessment
and management of financial risk. Chapter 18 provides a detailed and
in-depth study of this subject, reviewing the nature of cash-flow projec-
tions, the role of the actuarial valuation, the range of funding (or cost)
methods that have been proposed and implemented, and the different
approachestothevaluationofplanassets.Chapter18alsobrieflydiscusses
unfunded plans and how their costs may be managed. For defined-benefit
pension plans, a subject of equal importance to funding is the choice of
investmentstrategy,andthisisdiscussedinChapter19.Afterabriefreview
of the principal characteristics of the asset classes available, we consider
the investment objectives for different types of plan and the theoretical
and practical aspects of stochastic asset liability modeling.
Inmanyindustrializedcountries,thereisatrendtowardsgreaterpension
provisionthroughindividualaccumulationpoliciesordefined-contribution
plans. In both cases, the individual member may be responsible for critical
decisionsaffectinghowmuchiscontributedandhowitisinvested.Chapter
20looksattheseindividualchoices,presentingdeterministicandstochastic
approachestobenefitprojectionsintheaccumulationphase,preretirement.
We also consider postretirement choices for the pensioner in the
decumulation phase—for example, whether and when to buy an annuity
and the opportunities presented by income drawdown.
Part V considers actuarial theory and practice for Health Insurance.
It comprises an introductory chapter and four further chapters, each
devoted to one of the principal typesof insurance coverage. This approach
has been adopted in preference to considering the underlying processes of
underwriting, pricing, reserving, and claims management because these

processes vary markedly in practice between products and between
markets for a particular product line.
Chapter 21 provides an introduction to health insurance and considers
the principal contract types, contrasting these with life insurance. It looks
at some of the external factors that affect health insurance. It considers
the key contract features and the risks facing the insurance provider.
Chapter 22 deals with income protection insurance, a class of product
that providesincometo theinsuredwhilethey areunabletowork because
of illness or injury. Product design, underwriting, pricing, claim manage-
ment, and reserving are discussed. The section on pricing methodology
includes a brief review of some of the most widely used approaches, with
a focus on the multiple-state modeling framework.
Chapter 23 follows the structure of Chapter 22 but deals with critical
illnessinsurance,underwhichabenefitispayableuponthefirstoccurrence
© 2005 by Taylor & Francis Group, LLC