Health Insurance: Basic Actuarial Models

172 Pages·2014·3.42 MB·English

by  Ermanno Pitacco

EAA Series
Ermanno Pitacco
Health
Insurance
Basic Actuarial Models
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
Ermanno Pitacco
Health Insurance
Basic Actuarial Models
123
ErmannoPitacco
Universityof Trieste
Trieste
Italy
ISSN 1869-6929 ISSN 1869-6937 (electronic)
EAASeries
ISBN 978-3-319-12234-2 ISBN 978-3-319-12235-9 (eBook)
DOI 10.1007/978-3-319-12235-9
LibraryofCongressControlNumber:2014953582
MathematicsSubjectClassification:91B30,97M30
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Preface
The book aims at providing the “basics” of health insurance techniques. The first
chapters (Chaps. 1–3) explain the need for health insurance, the risks taken by an
insurance company writing health insurance policies, and describe insurance
productsinthisarea(sicknessinsurance,accidentinsurance,criticalillnesscovers,
incomeprotection,long-termcareinsurance,health-relatedbenefitsasriderstolife
insurance policies). Both individual and group policies are considered. Of course,
issues of specific current interest, e.g., the design of recent insurance products, are
also addressed.
Ashifttogeneralactuarialfeaturesofhealthinsuranceproductsfollows(Chap.4).
Then, basic actuarial models are presented for sickness insurance (Chap. 5) and
incomeprotection,i.e.,disabilityannuities(Chap.6);ashortintroductiontoactuarial
modelsforlong-termcareinsuranceproductsisalsoprovided.
Asregardsactuarialmodels,“basic”meansthatonlythetraditionalequivalence
principle is considered for premium and reserve calculations, whereas risk and
solvency issues are briefly addressed. Actually, the book aims at offering a com-
prehensiveintroductiontothebasicaspectsofpricingandreserving,thusproviding
the reader with the technical tools needed to move ahead in the field of health
insurance management.
The book has been planned and structured assuming as its target readers:
advanced undergraduate and graduate students in Actuarial Sciences; graduate
students in Economics, Business and Finance; professionals and technicians
operating in insurance and pension areas.
It is assumed 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). The mathematics has been kept at a
rather low level: indeed, almost all topics are presented in a “time-discrete”
framework, thus analytical tools like derivatives, integrals, etc., are not required.
Some sections in whichdifferential calculushas beenused canbeskippedwithout
significant loss in understanding the basic calculation principles.
v
vi Preface
Althoughthebookis“teaching”ratherthan“researchoriented”,manyscientific
andprofessionalcontributionstothehealthinsurancetechniquehavebeenincluded
intheReferences,suchaspapersinscientificjournalsandconferenceproceedings,
working papers, technical reports, etc. This material can provide substantial help,
especially if, for specific topics, textbooks are not available, or not updated. Cita-
tions,togetherwithsomecomments,arelistedinaspecialsectionattheendofeach
chapter.
Thelogicalstructureandthecontentsofthebookhavesuccessfullybeentested
in various teaching initiatives; in particular:
(cid:129) courses,shortcourses,andseminarsinseveraluniversities(UniversityofTrieste,
University of Louvain in Louvain-La-Neuve, European University at St.
Petersburg, MIB School of Management in Trieste);
(cid:129) seminarsforprofessionalbodies(PortugueseInstituteofActuaries,U.S.Society
ofActuaries,AustralianInstituteofActuaries,PolishSocietyofActuaries),inthe
framework of CPD (Continuing Professional Development);
(cid:129) CPD seminars in insurance companies (in Brussels and Lisbon).
If this book helps the reader to understand the basic technical features of the
products in the manifold areas of health insurance, and stimulates the reader’s
interest in deepening his/her knowledge of more complex topics, such as the risk
profile of health insurance portfolios, then it will have achieved its objective.
Acknowledgments
We would like tothank AG Insurancefor theirfinancial support.Partof this book
has been developed within the framework of the AG Insurance Chair on Health
Insurance at KU Leuven (chairholder: Jan Dhaene; co-chairholders: Katrien
Antonio, Michel Denuit).
Trieste, July 2014 Ermanno Pitacco
vii
Contents
1 The Individual Perspective: The Need for Health Insurance. . . . . . 1
1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Individual Cash-Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 The Time Profile of Health Care Costs. . . . . . . . . . . . 3
1.2.2 Risk Transfer via Insurance. . . . . . . . . . . . . . . . . . . . 4
1.2.3 Temporary Insurance Covers. . . . . . . . . . . . . . . . . . . 5
1.2.4 A Lifelong Insurance Cover. . . . . . . . . . . . . . . . . . . . 6
1.3 Financing Health-Related Expenses . . . . . . . . . . . . . . . . . . . . 9
1.4 Suggestions for Further Reading. . . . . . . . . . . . . . . . . . . . . . . 10
2 The Insurer’s Perspective: Managing Risks. . . . . . . . . . . . . . . . . . 11
2.1 The Risk Transfer Process. . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 The Risks Transferred to the Insurer. . . . . . . . . . . . . . 11
2.1.2 The Risk Transformation. . . . . . . . . . . . . . . . . . . . . . 12
2.1.3 Insurer’s Risk: Causes, Factors, Components. . . . . . . . 15
2.2 Risk Management Issues. . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 The RM Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Capital Allocation: Solvency Versus Value Creation. . . 20
2.3 Risks Inherent in the Random Lifetime. . . . . . . . . . . . . . . . . . 21
2.3.1 The Individual Lifetime. . . . . . . . . . . . . . . . . . . . . . . 21
2.3.2 The Longevity Dynamics . . . . . . . . . . . . . . . . . . . . . 23
2.3.3 Managing the Longevity Risk . . . . . . . . . . . . . . . . . . 26
2.4 Suggestions for Further Reading. . . . . . . . . . . . . . . . . . . . . . . 27
3 Health Insurance Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Products and Types of Benefits . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.1 Main Health Insurance Products. . . . . . . . . . . . . . . . . 30
3.2.2 The Policy Term . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.3 Monetary Benefits and Service Benefits . . . . . . . . . . . 32
3.2.4 Policy Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . 33
ix
x Contents
3.3 Accident Insurance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.1 Types of Benefits. . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.2 Other Features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4 Sickness Insurance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4.1 Types of Benefits. . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4.2 Some Policy Conditions . . . . . . . . . . . . . . . . . . . . . . 37
3.4.3 Other Features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5 Disability Insurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5.1 Type of Benefits in Individual Policies. . . . . . . . . . . . 39
3.5.2 Types of Benefits in Group Insurance
and Pension Plans . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.5.3 Benefit Amount and Policy Conditions. . . . . . . . . . . . 41
3.6 Long-Term Care Insurance . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.6.1 Measuring the Severity of Disability. . . . . . . . . . . . . . 42
3.6.2 LTCI Products: A Classification. . . . . . . . . . . . . . . . . 44
3.6.3 Fixed-Amount and Degree-Related Benefits. . . . . . . . . 44
3.6.4 Expense-Related Benefits . . . . . . . . . . . . . . . . . . . . . 50
3.6.5 Service Benefits. . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.7 Critical Illness Insurance. . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.7.1 Types of Benefits. . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.7.2 Multiple Critical Illness Benefits . . . . . . . . . . . . . . . . 52
3.8 Other Limited-Coverage Products. . . . . . . . . . . . . . . . . . . . . . 52
3.9 Combining Health and Life Benefits. . . . . . . . . . . . . . . . . . . . 53
3.9.1 Health Covers as Riders to Life Insurance. . . . . . . . . . 53
3.9.2 Health Covers in Insurance Packages . . . . . . . . . . . . . 54
3.10 Group Insurance in the Health Area . . . . . . . . . . . . . . . . . . . . 56
3.11 Public and Private Health Insurance . . . . . . . . . . . . . . . . . . . . 57
3.12 Microinsurance in the Health Area. . . . . . . . . . . . . . . . . . . . . 58
3.13 Suggestions for Further Reading. . . . . . . . . . . . . . . . . . . . . . . 61
4 Introduction to Actuarial Aspects . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.1 Some Preliminary Ideas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Technical Features of Premium Calculation. . . . . . . . . . . . . . . 64
4.2.1 Non-life Insurance Aspects . . . . . . . . . . . . . . . . . . . . 66
4.2.2 Life Insurance Aspects . . . . . . . . . . . . . . . . . . . . . . . 67
4.3 Suggestions for Further Reading. . . . . . . . . . . . . . . . . . . . . . . 68
5 Actuarial Models for Sickness Insurance. . . . . . . . . . . . . . . . . . . . 69
5.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2 One-year Covers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2.1 Notation and Assumptions. . . . . . . . . . . . . . . . . . . . . 69
5.2.2 From Equivalence Premiums to Gross Premiums . . . . . 71