Table Of ContentEAA Series
Annamaria Olivieri
Ermanno Pitacco
Introduction
to Insurance
Mathematics
Technical and Financial Features of
Risk Transfers
Second Edition
EAA Series
Editors-in-chief
Hansjoerg Albrecher University of Lausanne, Lausanne, Switzerland
Ulrich Orbanz University Salzburg, Salzburg, Austria
Editors
Michael Koller ETH Zurich, Zurich, Switzerland
Ermanno Pitacco Università di Trieste, Trieste, Italy
Christian Hipp Universität Karlsruhe, Karlsruhe, Germany
Antoon Pelsser Maastricht University, Maastricht, The Netherlands
Alexander J. McNeil Heriot-Watt University, Edinburgh, UK
EAAseriesissuccessoroftheEAALectureNotesandsupportedbytheEuropean
Actuarial Academy (EAA GmbH), founded on the 29 August, 2005 in Cologne
(Germany)bytheActuarialAssociationsofAustria,Germany,theNetherlandsand
Switzerland. EAA offers actuarial education including examination, permanent
education for certified actuaries and consulting on actuarial education.
actuarial-academy.com
More information about this series at http://www.springer.com/series/7879
Annamaria Olivieri Ermanno Pitacco
(cid:129)
Introduction to Insurance
Mathematics
Technical and Financial Features
of Risk Transfers
Second Edition
123
Annamaria Olivieri Ermanno Pitacco
Dipartimento di Economia DEAMS “BrunodeFinetti”
Universitàdi Parma Universitàdi Trieste
Parma Trieste
Italy Italy
ISSN 1869-6929 ISSN 1869-6937 (electronic)
EAA Series
ISBN978-3-319-21376-7 ISBN978-3-319-21377-4 (eBook)
DOI 10.1007/978-3-319-21377-4
LibraryofCongressControlNumber:2015947942
MathematicsSubjectClassification(2010):91B30
SpringerChamHeidelbergNewYorkDordrechtLondon
©SpringerInternationalPublishingSwitzerland2011,2015
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Foreword
ActuarialScience isadiscipline with afascinatingblendoftraditionalapproaches,
developed over many decades of experience, and modern techniques which are
available thanks to the fast development of statistical, computational, and mathe-
maticaltools,newinsightsintodependencemodeling,analysisofbigdata,financial
engineering, risk management, and insurance economics. At the same time the
insurance market is competitive and dynamic, and popular products are ever-more
complex mingling the actuarial and financial world to an extraordinary extent.
Whereas the life and non-life insurance markets are driven by somewhat dif-
ferent factors, each is equally challenging. Some life insurance products have an
extremely long duration, during which the economic environment can change
dramatically, and the underlying actuarial risks are typically themselves subject to
changes and developments. At the same time, despite a plethora of available data,
the amount of immediately relevant data to better understand a particular type of
riskisoftenlimitedanditisanartofitsowntodistinguishtherelevantonesfrom
the others.
This makes clear that the modern actuary needs a solid education in all these
fields. In particular, it is not only the learning offacts and available formulas and
procedures that need to be part of such an education, critical reflection about the
potential and limits of methods is also of ample importance in an ever-changing
actuarial environment, inwhich appropriate and robust decisions need tobe taken,
sometimes over long time horizons.
In Europe there is a good tradition for this type of approach, and the present
textbookinitssecondeditionisaniceexampleofit.Theauthorshavemanagedto
compile the standard introductory actuarial education material in a very accessible
and intuitive way, where the understanding of principles is in focus. For the next
step of technicalities, the reader is in each chapter targeted towards the respective
relevant literature. The book gives a well-structured overview of some of the most
important actuarial topics, deals with both traditional and recent challenges, in
particular for life insurance, and discusses related practical issues. The material is
alsoinlinewiththeneweducationsyllabusoftheActuarialAssociationofEurope.
v
vi Foreword
Altogether,withthepresentbookAnnamariaOlivieriandErmannoPitaccohave
succeeded to provide a gentle introduction to the field of Insurance Mathematics
that can be highly recommended to beginners for a first entry into the field, to
teachers as an accompanying textbook for introductory courses on the topic, and
last but not least to the experienced for the pleasure of reading!
Hansjörg Albrecher
University of Lausanne
Preface to the First Edition
This book aims at introducing technical and financial aspects of the insurance
business, with special emphasis on the actuarial valuation of insurance products.
While most of the presentation concerns life insurance, non-life insurance is also
addressed, as well as pension plans.
The book has been planned assuming as target readers:
(cid:129) advanced undergraduate and graduate students in Economics, Business, and
Finance;
(cid:129) advancedundergraduatestudentsinMathematicsandStatistics,possiblyaiming
at attending, after graduation, actuarial courses at a master’s level;
(cid:129) professionals and technicians operating in insurance and pension areas, whose
job may regard investments,risk analysis, financial reporting, and so on, hence
implying communication with actuarial professionals and managers.
Given the assumed target, the use of complex mathematical tools has been
avoided. In this sense, the book can be placed at some “midpoint” of the existing
literature, part of which adopts more formal approaches to insurance problems,
which implies the use of non-elementary mathematics and calculus, whereas
another part addresses practical questions totally avoiding even basic mathematics
(which, in our opinion, can conversely provide effective tools for presenting
technical and financial features of the insurance business).
We assume that the reader has attended courses providing basic notions of
Financial Mathematics (interest rates, compound interest, present values, accumu-
lations, annuities, etc.) and Probability (probability distributions, conditional
probabilities, expected value, variance, etc). As mentioned, Mathematics has been
kept at a rather low level. Indeed, almost all topics are presented in a “discrete”
framework,thusnotrequiringanalyticaltoolslikedifferentials,integrals,etc.Some
sections in which differential calculus has been used can be skipped, without sig-
nificant losses in understanding the following material.
Some details concerning the chapters of the book can help in explaining the
“rationale”underlyingitsstructureandthechoiceofthematerialsthereinincluded.
vii
viii PrefacetotheFirstEdition
Chapter 1 first aims at presenting the concept of risk, focusing in particular on
the(negative)consequencesofsomeeventswhichcanconcernaperson,afamily,a
firm, and so on. Second, the chapter describes the role of an insurance company,
which takes individual risks, builds up a pool of risks, and bears the risk of losses
caused by large numbers of events within the pool or unexpected severity of the
claims.
In Chapter 2 various aspects of the risk pooling process are addressed. The
effectsofcross-subsidy(and,inparticular,mutuality,andsolidarity)areillustrated.
Then,referringtoasimpleportfoliostructure,reinsurancearrangements,solvency,
and capital allocation are dealt with.
Hence,thefirsttwochaptersprovidethereader withanintroductiontoriskand
insurance. Indeed, a risk-management-oriented approach should underpin, in our
opinion, the teaching of the insurance technique and finance. It is worth stressing
that these two chapters can fulfill the syllabus of a very short course (say, 20–25
hours) aiming to present the basics of risk identification, risk assessment, and risk
management actions.
Chapters 3 to 7 focus on life insurance. Although many topics dealt with are
rather traditional (life tables, discounting cash-flows, premiums, and reserves for
various insurance products), several issues of great current interest have been
included;forexample,mortalitytrends,best-estimatereserving,riskmargins,profit
assessment, linking life insurance benefits to the investment performance,
unit-linked products, and so on.
Chapter 8 addresses problems related to the post-retirement income. In partic-
ular, defined contribution pension plans are addressed. The protection that an
individualcanobtainbyunderwritingappropriatebenefitsandfinancialguarantees,
before and after retirement, is examined. Special emphasis is placed on life annu-
itiesasanelementinpost-retirementincomearrangements.Risksemergingforthe
provider are described, with particular regard to financial and longevity risks.
Finally, Chapter 9 deals with non-life insurance. First, an overview of the
contentsofnon-lifeinsuranceproductsisprovided.Then,premiumcalculationand
relatedstatisticalbasesarefocused.IssuespresentedinChapter1areprogressed,in
order to introduce the stochastic modeling of claim frequency, claim severity, and
aggregate claim amounts. An introduction to technical reserves and profit assess-
ment concludes the chapter.
Each chapter concludes with a section providing bibliographic references and
suggestions for further reading. The list of references only includes textbooks and
monographs,whiledisregardingpapersinscientificjournals,congressproceedings,
researchandtechnicalreports,andsoon.Ourchoiceaimsatlimitingthenumberof
citations, in line with the teaching orientation of this work.
Wehavesuccessfullytestedthelogicalstructureandthecontentsofthebookin
various recent courses. In particular: a course on Insurance technique and finance
for graduate students in Finance at the University of Parma; a course on Life
insurance mathematics for undergraduate students in Statistics and undergraduate
studentsinMathematicsattheUniversityofTrieste;coursesonRiskandInsurance,
Life insurance technique, Non-life insurance technique and a distance-learning
PrefacetotheFirstEdition ix
courseonInsurancetechniqueforemployeesofaEuropeaninsurancecompany,at
theMIBSchoolofManagementinTrieste.Partofthematerialincludedinthebook
hasbeenusedalsoinCPD(ContinuingProfessionalDevelopment)coursesonLife
insurancetechniquefornon-actuariesorganizedbytheItalianactuarialprofessional
body.Further,somespecifictopicshavebeendeliveredinshortseminarsandother
teachinginitiatives(forexample:risk-managementapproachtoinsuranceproblems,
stochastic mortality, linking life insurance benefits to the investment performance,
etc).
Risks must be carefully identified, assessed, and managed by all the agents
(individuals, households, firms, public institutions, and so on). Risk transfer con-
stitutes an effective tool for managing risks, and the importance of insurers in this
transfer process is self-evident. Actually, the insurance business constitutes a
growing market. Appropriate risk management solutions must be taken also by
insurers, due to the risks they assume through their products.
Ifthisbookhelpstobetterunderstandthetechnicalandfinancialfeaturesofthe
insurance activity, the role of insurers as intermediaries in therisk pooling process
and as financial intermediaries, and the basics of the risk management of an
insurance business, then we have achieved our objective.
Trieste Annamaria Olivieri
July 2010 Ermanno Pitacco
