Introduction to Insurance Mathematics: Technical and Financial Features of Risk Transfers PDF
Preview Introduction to Insurance Mathematics: Technical and Financial Features of Risk Transfers
EAA 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 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper SpringerInternationalPublishingAGSwitzerlandispartofSpringerScience+BusinessMedia (www.springer.com) 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
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