Introduction to insurance mathematics: technical and financial features of risk transfers
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
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Berlin [u.a.]
Springer
2011
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| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XV, 463 S. graph. Darst. |
| ISBN: | 9783642160288 |
Internformat
MARC
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| 245 | 1 | 0 | |a Introduction to insurance mathematics |b technical and financial features of risk transfers |c Annamaria Olivieri ; Ermanno Pitacco |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2011 | |
| 300 | |a XV, 463 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
RISKS AND INSURANCE 1
1.1 INTRODUCTION 1
1.2 "RISK": LOOKING FOR DEFINITIONS 1
1.2.1 SOME PRELIMINARY IDEAS 1
1.2.2 TRANSACTIONS WITH RANDOM RESULTS 2
1.2.3 A VERY BASIC INSURABLE RISK 4
1.2.4 RANDOM NUMBER OF EVENTS AND RANDOM AMOUNTS 4 1.2.5 RISKS INHERENT
IN THE INDIVIDUAL LIFETIME 9
1.3 MANAGING RISKS 14
1.3.1 GENERAL ASPECTS 14
1.3.2 RISK IDENTIFICATION AND RISK ASSESSMENT 15
1.3.3 RISK MANAGEMENT ACTIONS 16
1.3.4 SELF-INSURANCE VERSUS INSURANCE 18
1.3.5 MONITORING AND THE RISK MANAGEMENT CYCLE 21
1.4 QUANTIFYING RISKS: SOME MODELS 21
1.4.1 SOME PRELIMINARY IDEAS 21
1.4.2 A VERY BASIC MODEL 22
1.4.3 RANDOM NUMBER OF EVENTS AND RANDOM AMOUNTS 23 1.4.4 RANDOM SUMS: A
CRITICAL ASSUMPTION 28
1.4.5 INTRODUCING TIME INTO VALUATIONS 29
1.4.6 COMPARING RANDOM YIELDS 31
1.4.7 RISK-ADJUSTED VALUATIONS 33
1.5 RISK MEASURES 37
1.5.1 SOME PRELIMINARY IDEAS 37
1.5.2 TRADITIONAL RISK MEASURES 38
1.5.3 DOWNSIDE RISK MEASURES 39
1.5.4 RISK MEASURES AND CAPITAL REQUIREMENTS 40
1.6 TRANSFERRING RISKS 43
1.6.1 BUILDING UP A POOL 43
1.6.2 FINANCING THE POOL 46
1.6.3 THE ROLE OF THE INSURER 51
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1006508066
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
1.7 INSURANCE PRODUCTS 53
1.7.1 THE INSURANCE COVER. POLICY CONDITIONS 53
1.7.2 SOME EXAMPLES 54
1.7.3 PRICING INSURANCE PRODUCTS 56
1.7.4 PREMIUM CALCULATION 57
1.7.5 TECHNICAL BASES 64
1.7.6 RESERVING 66
1.8 REFERENCES AND SUGGESTIONS FOR FURTHER READING 67
MANAGING A PORTFOLIO OF RISKS 69
2.1 INTRODUCTION 69
2.2 RATING: THE BASICS 70
2.2.1 SOME PRELIMINARY IDEAS 70
2.2.2 HOMOGENEOUS RISKS 70
2.2.3 NON-HOMOGENEOUS RISKS 71
2.2.4 A MORE GENERAL RATING SYSTEM 72
2.2.5 RATING SYSTEMS AND TECHNICAL EQUILIBRIUM 73
2.2.6 FROM RISK FACTORS TO RATING CLASSES 75
2.2.7 CROSS-SUBSIDY: MUTUALITY AND SOLIDARITY 77
2.3 FACING PORTFOLIO RISKINESS 78
2.3.1 EXPECTED OUTGO VERSUS ACTUAL OUTGO 79
2.3.2 RISK ASSESSMENT 80
2.3.3 THE RISK INDEX 82
2.3.4 THE PROBABILITY DISTRIBUTION OF THE TOTAL PAYMENT 84 2.3.5 THE
SAFETY LOADING 87
2.3.6 CAPITAL ALLOCATION AND BEYOND 91
2.3.7 SOLVENCY 94
2.3.8 CREATING VALUE 95
2.3.9 RISK MANAGEMENT AND RISK ANALYSIS: SOME REMARKS 97 2.3.10 THE
"UNCERTAINTY RISK" 98
2.4 REINSURANCE: THE BASICS 101
2.4.1 GENERAL ASPECTS 101
2.4.2 STOP-LOSS REINSURANCE 103
2.4.3 FROM PORTFOLIOS TO CONTRACTS 105
2.4.4 TWO REINSURANCE ARRANGEMENTS 107
2.4.5 EXAMPLES 109
2.4.6 OPTIMAL REINSURANCE POLICY I LL
2.5 REINSURANCE: FURTHER ASPECTS 113
2.5.1 REINSURANCE ARRANGEMENTS 113
2.5.2 RANDOM CLAIM SIZES. XL REINSURANCE 114
2.5.3 CATASTROPHE REINSURANCE 116
2.5.4 PURPOSES OF REINSURANCE 118
2.5.5 INSURANCE-REINSURANCE NETWORKS 119
2.5.6 REINSURANCE TREATIES. REINSURANCE PROGRAMMES 120 2.6 ALTERNATIVE
RISK TRANSFERS 123
IMAGE 3
CONTENTS
2.6.1 SOME PRELIMINARY IDEAS 123
2.6.2 SECURITIZATION AND THE ROLE OF CAPITAL MARKETS 124 2.6.3 AN
EXAMPLE: THE MORTALITY BONDS 126
2.7 THE TIME DIMENSION 128
2.7.1 GENERAL ASPECTS 128
2.7.2 PREMIUMS, PAYMENTS, PORTFOLIO FUND 130
2.7.3 SOLVENCY AND CAPITAL REQUIREMENTS 131
2.7.4 GENERALIZING THE MODEL 134
2.7.5 SOLVENCY AND CAPITAL FLOWS 135
2.8 REFERENCES AND SUGGESTIONS FOR FURTHER READING 137
2.A APPENDIX 138
LIFE INSURANCE: MODELING THE LIFETIME 141
3.1 INTRODUCTION 141
3.2 LIFE TABLES 141
3.2.1 ELEMENTS OF A LIFE TABLE 141
3.2.2 COHORT TABLES AND PERIOD TABLES 142
3.2.3 CONSTRUCTION OF A PERIOD LIFE TABLE 145
3.2.4 "POPULATION" TABLES VERSUS "MARKET" TABLES 147
3.2.5 THE LIFE TABLE AS A PROBABILISTIC MODEL 148
3.2.6 ONE-YEAR MEASURES OF MORTALITY 149
3.2.7 A MORE FORMAL SETTING: THE RANDOM LIFETIME 153
3.3 SUMMARIZING A LIFE TABLE 154
3.3.1 THE LIFE EXPECTANCY 154
3.3.2 OTHER MARKERS 156
3.4 A MORTALITY "LAW" 156
3.4.1 FROM TABLES TO PARAMETERS 156
3.4.2 THE HELIGMAN-POLLARD LAW 157
3.5 FROM THE BASIC MODEL TO MORE GENERAL MODELS 159
3.6 HETEROGENEITY 159
3.6.1 SOME PRELIMINARY IDEAS 159
3.6.2 RATING CLASSES 161
3.6.3 SUBSTANDARD RISKS 163
3.6.4 THE "FACTOR FORMULA" 164
3.7 MORTALITY BY AGE AND DURATION 165
3.7.1 SOME PRELIMINARY IDEAS 165
3.7.2 SELECT TABLES AND ULTIMATE TABLES 166
3.7.3 A PRACTICAL ISSUE 168
3.8 MORTALITY DYNAMICS 168
3.8.1 MORTALITY TRENDS 168
3.8.2 REPRESENTING MORTALITY DYNAMICS 171
3.8.3 PROBABILITIES AND LIFE EXPECTANCY IN A DYNAMIC CONTEXT 173 3.8.4
APPROACHES TO MORTALITY FORECASTS 174
3.8.5 EXTRAPOLATION VIA EXPONENTIAL FORMULAE 176
3.8.6 MORTALITY FORECASTS ALLOWING FOR RANDOM FLUCTUATIONS 178
IMAGE 4
CONTENTS
3.9 MOVING TO A TIME-CONTINUOUS CONTEXT 179
3.9.1 THE SURVIVAL FUNCTION 180
3.9.2 OTHER RELATED FUNCTIONS 181
3.9.3 THE FORCE OF MORTALITY 183
3.9.4 MARKERS 184
3.9.5 PARAMETRIC MODELS 186
3.10 STOCHASTIC MORTALITY 188
3.10.1 NUMBER OF PEOPLE ALIVE IN A COHORT 188
3.10.2 DETERMINISTIC MODELS VERSUS STOCHASTIC MODELS 188 3.10.3 RANDOM
FLUCTUATIONS IN MORTALITY 191
3.10.4 SYSTEMATIC DEVIATIONS IN MORTALITY 192
3.10.5 THE IMPACT OF MORTALITY / LONGEVITY RISK ON LIFE INSURANCE . .
193 3.11 REFERENCES AND SUGGESTIONS FOR FURTHER READING 194
LIFE INSURANCE: PRICING 197
4.1 LIFE INSURANCE PRODUCTS 197
4.1.1 GENERAL ASPECTS 197
4.1.2 ALTERATIONS OF A LIFE INSURANCE CONTRACT 199
4.2 DISCOUNTING CASH-FLOWS 200
4.2.1 PREMIUMS, BENEFITS, EXPENSES 200
4.2.2 A LUMP SUM BENEFIT IN THE CASE OF DEATH 202
4.2.3 A LUMP SUM BENEFIT IN THE CASE OF SURVIVAL 202
4.2.4 COMBINING BENEFITS 202
4.2.5 ACTUARIAL VALUES: TERMINOLOGY AND NOTATION 204
4.2.6 ACTUARIAL VALUES: INEQUALITIES 207
4.2.7 ACTUARIAL VALUES WITH ZERO INTEREST RATE 207
4.2.8 THE ACTUARIAL DISCOUNT FACTOR 208
4.2.9 ACTUARIAL VALUES: FURTHER RELATIONS 209
4.2.10 ACTUARIAL VALUES AT TIMES FOLLOWING THE POLICY ISSUE 210 4.3
SINGLE PREMIUMS 211
4.3.1 THE EQUIVALENCE PRINCIPLE 211
4.3.2 THE PURE ENDOWMENT 213
4.3.3 LIFE ANNUITIES 215
4.3.4 THE TERM INSURANCE 217
4.3.5 THE WHOLE LIFE INSURANCE 219
4.3.6 COMBINING SURVIVAL AND DEATH BENEFITS 220
4.3.7 ENDOWMENT INSURANCE PRODUCTS 221
4.3.8 THE EXPECTED PROFIT: A FIRST INSIGHT 224
4.4 PERIODIC PREMIUMS 226
4.4.1 AN EXAMPLE 226
4.4.2 LEVEL PREMIUMS 229
4.4.3 NATURAL PREMIUMS 230
4.4.4 SINGLE PREMIUM, NATURAL PREMIUMS AND LEVEL PREMIUMS: SOME
RELATIONS 233
4.4.5 SINGLE RECURRENT PREMIUMS 234
IMAGE 5
CONTENTS
4.4.6 SOME CONCLUDING REMARKS 237
4.5 LOADING FOR EXPENSES 238
4.5.1 PREMIUM COMPONENTS 238
4.5.2 EXPENSES AND LOADING FOR EXPENSES 239
4.5.3 THE EXPENSE-LOADED PREMIUMS 240
4.6 REFERENCES AND SUGGESTIONS FOR FURTHER READING 243
LIFE INSURANCE: RESERVING 245
5.1 INTRODUCTION 245
5.2 GENERAL ASPECTS 245
5.3 THE POLICY RESERVE 247
5.3.1 DEFINITION 247
5.3.2 THE POLICY RESERVE FOR SOME INSURANCE PRODUCTS 248 5.3.3 THE TIME
PROFILE OF THE POLICY RESERVE 249
5.3.4 CHANGE IN THE TECHNICAL BASIS 256
5.3.5 THE RESERVE AT FRACTIONAL DURATIONS 259
5.3.6 THE RETROSPECTIVE RESERVE 263
5.3.7 THE ACTUARIAL ACCUMULATION PROCESS 265
5.4 RISK AND SAVINGS 267
5.4.1 A (RATHER) GENERAL INSURANCE PRODUCT 267
5.4.2 RECURSIVE EQUATIONS 268
5.4.3 RISK PREMIUM AND SAVINGS PREMIUM 270
5.4.4 LIFE INSURANCE PRODUCTS VERSUS FINANCIAL ACCUMULATION 274 5.5
EXPECTED PROFITS: A FURTHER INSIGHT 277
5.5.1 EXPECTED ANNUAL PROFITS 277
5.5.2 SPLITTING THE ANNUAL PROFIT 278
5.5.3 THE EXPECTED TOTAL PROFIT 280
5.5.4 CASH-FLOWS, PROFITS, PREMIUM MARGINS 282
5.5.5 EXPECTED PROFITS ACCORDING TO BEST-ESTIMATE RESERVING 285 5.6
RESERVING FOR EXPENSES 286
5.7 SURRENDER VALUES AND PAID-UP VALUES 288
5.8 REFERENCES AND SUGGESTIONS FOR FURTHER READING 290
RESERVES AND PROFITS IN A LIFE INSURANCE PORTFOLIO 291
6.1 THE PORTFOLIO RESERVE 291
6.1.1 FUTURE PORTFOLIO RESERVES 292
6.1.2 SAFE-SIDE RESERVE VERSUS BEST-ESTIMATE RESERVE 293 6.1.3 THE RISK
MARGIN 294
6.1.4 THE PORTFOLIO LIABILITY AND BEYOND 297
6.1.5 RISK MARGIN: THE "COST OF CAPITAL" APPROACH 298
6.2 THE TOTAL PROFIT 300
6.2.1 THE LIFE FUND 300
6.2.2 THE EXPECTED LIFE FUND AND THE EXPECTED TOTAL PROFIT 301 6.2.3 THE
TOTAL PROFIT: AN ALTERNATIVE INTERPRETATION 304 6.3 EXPECTED ANNUAL
PROFITS 305
IMAGE 6
CONTENTS
6.3.1 THE EXPECTED SURPLUS AND THE EXPECTED ANNUAL PROFITS 306 6.3.2 THE
ROLE OF THE PORTFOLIO RESERVE 308
6.4 EXPECTED ANNUAL PROFITS: A MORE GENERAL SETTING 312
6.5 REFERENCES AND SUGGESTIONS FOR FURTHER READING 316
FINANCE IN LIFE INSURANCE: LINKING BENEFITS TO THE INVESTMENT
PERFORMANCE 317
7.1 INTRODUCTION 317
7.2 ADJUSTING BENEFITS 319
7.2.1 THE GENERAL CASE 319
7.2.2 ADDRESSING SPECIFIC INSURANCE PRODUCTS 322
7.2.3 IMPLEMENTING SOLUTIONS 327
7.2.4 THE YIELD TO MATURITY FOR THE POLICYHOLDER 331
7.3 PARTICIPATING POLICIES 335
7.3.1 PARTICIPATING POLICIES WITH A GUARANTEED ANNUAL RETURN 336 7.3.2
PARTICIPATING POLICIES WITH A GUARANTEED AVERAGE RETURN 341 7.4
UNIT-LINKED POLICIES 346
7.4.1 DEFINITION OF UNIT-LINKED BENEFITS 347
7.4.2 UNIT-LINKED POLICIES WITHOUT GUARANTEES 348
7.4.3 UNIT-LINKED POLICIES WITH FINANCIAL GUARANTEES 353 7.5 FINANCIAL
OPTIONS IN UNIT-LINKED AND PARTICIPATING POLICIES 356 7.5.1 THE
STRUCTURE OF MINIMUM GUARANTEES 356
7.5.2 THE VALUATION OF FINANCIAL OPTIONS IN A UNIT-LINKED POLICY . .
358 7.6 WITH-PROFIT POLICIES 360
7.7 INDEX-LINKED POLICIES 363
7.8 UNIVERSAL LIFE POLICIES 365
7.9 VARIABLE ANNUITIES 366
7.10 REFERENCES AND SUGGESTIONS FOR FURTHER READING 371
PENSION PLANS: TECHNICAL AND FINANCIAL PERSPECTIVES 373 8.1 INTRODUCTION
373
8.2 PENSION PROGRAMMES 374
8.2.1 INDIVIDUAL AND GROUP PENSION PLANS 374
8.2.2 BENEFITS AND CONTRIBUTIONS 376
8.2.3 TIMING OF THE FUNDING 378
8.3 TRANSFERRING RISKS TO THE PROVIDER 379
8.4 PENSION SAVINGS BEFORE RETIREMENT 381
8.5 ARRANGING THE POST-RETIREMENT INCOME 381
8.5.1 SOME BASIC FEATURES OF LIFE ANNUITIES 381
8.5.2 PACKAGING BENEFITS INTO THE LIFE ANNUITY PRODUCT 382 8.5.3 LIFE
ANNUITIES VERSUS INCOME DRAWDOWN 383
8.5.4 PHASED RETIREMENT 386
8.6 RISKS FOR THE PROVIDER 388
8.7 REFERENCES AND SUGGESTIONS FOR FURTHER READING 392
IMAGE 7
CONTENTS XV
9 NON-LIFE INSURANCE: PRICING AND RESERVING 395
9.1 INTRODUCTION 395
9.2 NON-LIFE INSURANCE PRODUCTS 396
9.2.1 GENERAL ASPECTS 396
9.2.2 MAIN CATEGORIES OF NON-LIFE INSURANCE PRODUCTS 396 9.3 LOSS AND
CLAIM AMOUNT 398
9.4 THE EQUIVALENCE PREMIUM 402
9.4.1 THE ITEMS OF THE EQUIVALENCE PREMIUM 402
9.4.2 THE TIME-PATTERN OF A CLAIM 402
9.4.3 THE EXPECTED AGGREGATE CLAIM AMOUNT 403
9.5 THE NET PREMIUM 405
9.6 THE EXPENSE-LOADED PREMIUM 408
9.7 STATISTICAL DATA FOR THE EQUIVALENCE PREMIUM 409
9.7.1 RISK PREMIUM, CLAIM FREQUENCY, LOSS SEVERITY 409 9.7.2 UNITS OF
EXPOSURE: THE CASE OF HETEROGENEOUS PORTFOLIOS .411 9.7.3 UNITS OF
EXPOSURE: THE NUMBER OF POLICY YEARS 413
9.7.4 UPDATING THE RISK PREMIUM TO PORTFOLIO EXPERIENCE 416 9.8
STOCHASTIC MODELING OF THE AGGREGATE CLAIM AMOUNT 420 9.8.1 MODELING THE
CLAIM FREQUENCY 420
9.8.2 MODELING THE CLAIM SEVERITY 424
9.8.3 MODELING THE AGGREGATE CLAIM AMOUNT 425
9.9 RISK CLASSIFICATION AND EXPERIENCE-RATING 428
9.9.1 RISK CLASSES AND RATING CLASSES 428
9.9.2 RISK CLASSIFICATION AT ISSUE 429
9.9.3 RISK CLASSIFICATION AT RENEWAL TIMES: INDIVIDUAL EXPERIENCE RATING
430
9.10 TECHNICAL RESERVES: AN INTRODUCTION 434
9.11 EARNED PREMIUMS, INCURRED CLAIM AMOUNTS AND PROFIT ASSESSMENT.
438 9.12 DETERMINISTIC MODELS FOR CLAIM RESERVES 441
9.12.1 RUN-OFF TRIANGLES 442
9.12.2 THE EXPECTED LOSS RATIO METHOD 443
9.12.3 THE CHAIN-LADDER METHOD 444
9.12.4 THE BORNHUETTER-FERGUSON METHOD 446
9.12.5 FURTHER ASPECTS 448
9.13 REFERENCES AND SUGGESTIONS FOR FURTHER READING 449
REFERENCES 451
INDEX 455 |
| any_adam_object | 1 |
| author | Olivieri, Annamaria Pitacco, Ermanno 1947-2022 |
| author_GND | (DE-588)138165246 |
| author_facet | Olivieri, Annamaria Pitacco, Ermanno 1947-2022 |
| author_role | aut aut |
| author_sort | Olivieri, Annamaria |
| author_variant | a o ao e p ep |
| building | Verbundindex |
| bvnumber | BV037228796 |
| classification_rvk | QQ 630 SK 980 |
| ctrlnum | (OCoLC)711824223 (DE-599)DNB1006508066 |
| dewey-full | 368.01 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 368 - Insurance |
| dewey-raw | 368.01 |
| dewey-search | 368.01 |
| dewey-sort | 3368.01 |
| dewey-tens | 360 - Social problems and services; associations |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV037228796 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T10:58:48Z |
| institution | BVB |
| isbn | 9783642160288 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021142518 |
| oclc_num | 711824223 |
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| owner_facet | DE-523 DE-384 DE-11 DE-19 DE-BY-UBM DE-824 DE-861 DE-188 |
| physical | XV, 463 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| spelling | Olivieri, Annamaria Verfasser aut Introduction to insurance mathematics technical and financial features of risk transfers Annamaria Olivieri ; Ermanno Pitacco Berlin [u.a.] Springer 2011 XV, 463 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Versicherungsmathematik (DE-588)4063194-1 s DE-604 Pitacco, Ermanno 1947-2022 Verfasser (DE-588)138165246 aut Erscheint auch als Online-Ausgabe 978-3-642-16029-5 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3532048&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021142518&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Olivieri, Annamaria Pitacco, Ermanno 1947-2022 Introduction to insurance mathematics technical and financial features of risk transfers Versicherungsmathematik (DE-588)4063194-1 gnd |
| subject_GND | (DE-588)4063194-1 (DE-588)4123623-3 |
| title | Introduction to insurance mathematics technical and financial features of risk transfers |
| title_auth | Introduction to insurance mathematics technical and financial features of risk transfers |
| title_exact_search | Introduction to insurance mathematics technical and financial features of risk transfers |
| title_full | Introduction to insurance mathematics technical and financial features of risk transfers Annamaria Olivieri ; Ermanno Pitacco |
| title_fullStr | Introduction to insurance mathematics technical and financial features of risk transfers Annamaria Olivieri ; Ermanno Pitacco |
| title_full_unstemmed | Introduction to insurance mathematics technical and financial features of risk transfers Annamaria Olivieri ; Ermanno Pitacco |
| title_short | Introduction to insurance mathematics |
| title_sort | introduction to insurance mathematics technical and financial features of risk transfers |
| title_sub | technical and financial features of risk transfers |
| topic | Versicherungsmathematik (DE-588)4063194-1 gnd |
| topic_facet | Versicherungsmathematik Lehrbuch |
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