Life insurance mathematics: with exercises
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German English |
| Published: |
Berlin u.a.
Springer
1995
|
| Edition: | 2., expanded ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 217 S. graph. Darst. |
| ISBN: | 3540588582 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV010386859 | ||
| 003 | DE-604 | ||
| 005 | 20050608 | ||
| 007 | t | ||
| 008 | 950911s1995 gw d||| |||| 00||| ger d | ||
| 016 | 7 | |a 94536119X |2 DE-101 | |
| 020 | |a 3540588582 |c Gb. : DM 78.00 |9 3-540-58858-2 | ||
| 035 | |a (OCoLC)634459820 | ||
| 035 | |a (DE-599)BVBBV010386859 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a ger |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-91 |a DE-824 |a DE-859 |a DE-898 |a DE-91G |a DE-83 |a DE-11 | ||
| 084 | |a QQ 600 |0 (DE-625)141985: |2 rvk | ||
| 084 | |a SK 980 |0 (DE-625)143277: |2 rvk | ||
| 084 | |a WIR 190f |2 stub | ||
| 084 | |a 62P05 |2 msc | ||
| 084 | |a MAT 902f |2 stub | ||
| 100 | 1 | |a Gerber, Hans U. |d 1943- |e Verfasser |0 (DE-588)110122666 |4 aut | |
| 240 | 1 | 0 | |a Lebensversicherungsmathematik |
| 245 | 1 | 0 | |a Life insurance mathematics |b with exercises |c Hans U. Gerber |
| 250 | |a 2., expanded ed. | ||
| 264 | 1 | |a Berlin u.a. |b Springer |c 1995 | |
| 300 | |a XV, 217 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lebensversicherung |0 (DE-588)4034928-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Versicherungsmathematik |0 (DE-588)4063194-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lebensversicherung |0 (DE-588)4034928-7 |D s |
| 689 | 0 | 1 | |a Versicherungsmathematik |0 (DE-588)4063194-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Lebensversicherung |0 (DE-588)4034928-7 |D s |
| 689 | 1 | 1 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006916085&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006916085 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804124812572884992 |
|---|---|
| adam_text | I
Contents
1 The Mathematics of Compound Interest
1.1 Mathematical Bases of Life Contingencies 1
1.2 Effective Interest Rates 1
1.3 Nominal Interest Rates 2
1.4 Continuous Payments 3
1.5 Interest in Advance 4
1.6 Perpetuities 6
1.7 Annuities 9
1.8 Repayment of a Debt 11
1.9 Internal Rate of Return 13
2 The Future Lifetime of a Life Aged x
2.1 The Model 15
2.2 The Force of Mortality 16
2.3 Analytical Distributions of T 17
2.4 The Curtate Future Lifetime of (a;) 18
2.5 Life Tables 20
2.6 Probabilities of Death for Fractions of a Year 21
3 Life Insurance
3.1 Introduction 23
3.2 Elementary Insurance Types 23
3.2.1 Whole Life and Term Insurance 23
3.2.2 Pure Endowments 24
3.2.3 Endowments 25
3.3 Insurances Payable at the Moment of Death 26
3.4 General Types of Life Insurance 27
3.5 Standard Types of Variable Life Insurance 29
3.6 Recursive Formulae 31
4 Life Annuities
4.1 Introduction 35
4.2 Elementary Life Annuities 35
XII Contents
4.3 Payments made more Frequently tJlhan Once a Year 37
4.4 Variable Life Annuities 39
4.5 Standard Types of Life Annuity . 41
4.6 Recursion Formulae 42
4.7 Inequalities 43
4.8 Payments Starting at Non integral Ages 46
5 Net Premiums
5.1 Introduction 49
5.2 An Example 49
5.3 Elementary Forms of Insurance 52
5.3.1 Whole Life and Term Insurafince 52
5.3.2 Pure Endowments 53
5.3.3 Endowments 54
5.3.4 Deferred Life Annuities ... 54
5.4 Premiums Paid m Times a Year 54
5.5 A General Type of Life Insurance 55
5.6 Policies with Premium Refund ... 56
5.7 Stochastic Interest 56
6 Net Premium Reserves
6.1 Introduction 59
6.2 Two Examples 59
6.3 Recursive Considerations 61
6.4 The Survival Risk 63
6.5 The Net Premium Reserve of a Wholfle Life Insurance 63
6.6 Net Premium Reserves at Fractional Durations 64
6.7 Allocation of the Overall Loss to Polilcy Years 65
6.8 Conversion of an Insurance 68
6.9 Technical Gain 69
6.10 Procedure for Pure Endowments ... 70
6.11 The Continuous Model 71
7 Multiple Decrements
7.1 The Model 75
7.2 Forces of Decrement 76
7.3 The Curtate Lifetime of (x) 76
7.4 A General Type of Insurance 77
7.5 The Net Premium Reserve 78
7.6 The Continuous Model 80
I
Contents XIII
8 Multiple Life Insurance
8.1 Introduction 83
8.2 The Joint Life Status 83
8.3 Simplifications 84
8.4 The Last Survivor Status 85
8.5 The General Symmetric Status 87
8.6 The Schuette Nesbitt Formula 89
8.7 Asymmetric Annuities 90
8.8 Asymmetric Insurances 91
9 The Total Claim Amount in a Portfolio
9.1 Introduction 93
9.2 The Normal Approximation 93
9.3 Exact Calculation of the Total Claim Amount Distribution . . 94
9.4 The Compound Poisson Approximation 96
9.5 Recursive Calculation of the Compound Poisson Distribution . 98
9.6 Reinsurance 100
9.7 Stop Loss Reinsurance 101
10 Expense Loadings
10.1 Introduction 103
10.2 The Expense Loaded Premium 104
10.3 Expense Loaded Premium Reserves 105
11 Estimating Probabilities of Death
11.1 Problem Description 109
11.2 The Classical Method 110
11.3 Alternative Solution Ill
11.4 The Maximum Likelihood Method 112
11.5 Statistical Inference 112
11.6 The Bayesian Approach 116
11.7 Multiple Causes of Decrement 116
11.8 Interpretation of Results 118
Appendix A. Commutation Functions
A.I Introduction 119
A.2 The Deterministic Model 119
A.3 Life Annuities 120
A.4 Life Insurance 121
A.5 Net Annual Premiums and Premium Reserves 122
Appendix B. Simple Interest 125
XIV Contents
Appendix C. Exercises
CO Introduction 128
C.I Mathematics of Compound Interest: Exercises 129
C.I.I Theory Exercises 129
C.1.2 Spreadsheet Exercises 130
C.2 The Future Lifetime of a Life Aged x: Exercises 133
C.2.1 Theory Exercises 134
C.2.2 Spreadsheet Exercises 136
C.3 Life Insurance 138
C.3.1 Theory Exercises 138
C.3.2 Spreadsheet Exercises 141
C.4 Life Annuities 142
C.4.1 Theory Exercises 142
C.4.2 Spreadsheet Exercises 144
C.5 Net Premiums 146
C.5.1 Notes 146
C.5.2 Theory Exercises 146
C.5.3 Spreadsheet Exercises 150
C.6 Net Premium Reserves 152
C.6.1 Theory Exercises 152
C.6.2 Spreadsheet Exercises 155
C.7 Multiple Decrements: Exercises 156
C.7.1 Theory Exercises 156
C.8 Multiple Life Insurance: Exercises 158
C.8.1 Theory Exercises 158
C.8.2 Spreadsheet Exercises 160
C.9 The Total Claim Amount in a Portfolio 161
C.9.1 Theory Exercises 161
CIO Expense Loadings 163
C.10.1 Theory Exercises 163
CIO.2 Spreadsheet Exercises 164
Cll Estimating Probabilities of Death 165
C.ll.l Theory Exercises 165
Appendix D. Solutions
D.O Introduction 168
D.I Mathematics of Compound Interest 169
D.I.I Solutions to Theory Exercises 169
D.I.2 Solutions to Spreadsheet Exercises 170
D.2 The Future Lifetime of a Life Aged x 172
D.2.1 Solutions to Theory Exercise 172
D.2.2 Solutions to Spreadsheet Exercises 174
D.3 Life Insurance 175
D.3.1 Solutions to Theory Exercises 175
D.3.2 Solution to Spreadsheet Exercises 178
Contents XV
D.4 Life Annuities 179
D.4.1 Solutions to Theory Exercises 179
D.4.2 Solutions to Spreadsheet Exercises 181
D.5 Net Premiums: Solutions 183
D.5.1 Theory Exercises 183
D.5.2 Solutions to Spreadsheet Exercises 187
D.6 Net Premium Reserves: Solutions 189
D.6.1 Theory Exercises 189
D.6.2 Solutions to Spreadsheet Exercises 190
D.7 Multiple Decrements: Solutions 192
D.7.1 Theory Exercises 192
D.8 Multiple Life Insurance: Solutions 194
D.8.1 Theory Exercises 194
D.8.2 Solutions to Spreadsheet Exercises 197
D.9 The Total Claim Amount in a Portfolio 198
D.9.1 Theory Exercises 198
D.10 Expense Loadings 200
D.10.1 Theory Exercises 200
D.10.2 Spreadsheet Exercises 201
D.ll Estimating Probabilities of Death 203
D.ll.l Theory Exercises 203
Appendix E. Tables
E.O Illustrative Life Tables 207
E. 1 Commutation Columns 209
E.2 Multiple Decrement Tables 211
References 213
Index 215
|
| any_adam_object | 1 |
| author | Gerber, Hans U. 1943- |
| author_GND | (DE-588)110122666 |
| author_facet | Gerber, Hans U. 1943- |
| author_role | aut |
| author_sort | Gerber, Hans U. 1943- |
| author_variant | h u g hu hug |
| building | Verbundindex |
| bvnumber | BV010386859 |
| classification_rvk | QQ 600 SK 980 |
| classification_tum | WIR 190f MAT 902f |
| ctrlnum | (OCoLC)634459820 (DE-599)BVBBV010386859 |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2., expanded ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01929nam a2200493 c 4500</leader><controlfield tag="001">BV010386859</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20050608 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">950911s1995 gw d||| |||| 00||| ger d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">94536119X</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540588582</subfield><subfield code="c">Gb. : DM 78.00</subfield><subfield code="9">3-540-58858-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)634459820</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010386859</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">ger</subfield><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-859</subfield><subfield code="a">DE-898</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">QQ 600</subfield><subfield code="0">(DE-625)141985:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 980</subfield><subfield code="0">(DE-625)143277:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">WIR 190f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">62P05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 902f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Gerber, Hans U.</subfield><subfield code="d">1943-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)110122666</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Lebensversicherungsmathematik</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Life insurance mathematics</subfield><subfield code="b">with exercises</subfield><subfield code="c">Hans U. Gerber</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2., expanded ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin u.a.</subfield><subfield code="b">Springer</subfield><subfield code="c">1995</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 217 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lebensversicherung</subfield><subfield code="0">(DE-588)4034928-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Versicherungsmathematik</subfield><subfield code="0">(DE-588)4063194-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Lebensversicherung</subfield><subfield code="0">(DE-588)4034928-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Versicherungsmathematik</subfield><subfield code="0">(DE-588)4063194-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Lebensversicherung</subfield><subfield code="0">(DE-588)4034928-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006916085&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-006916085</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV010386859 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:51:37Z |
| institution | BVB |
| isbn | 3540588582 |
| language | German English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006916085 |
| oclc_num | 634459820 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-824 DE-859 DE-898 DE-BY-UBR DE-91G DE-BY-TUM DE-83 DE-11 |
| owner_facet | DE-91 DE-BY-TUM DE-824 DE-859 DE-898 DE-BY-UBR DE-91G DE-BY-TUM DE-83 DE-11 |
| physical | XV, 217 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| spelling | Gerber, Hans U. 1943- Verfasser (DE-588)110122666 aut Lebensversicherungsmathematik Life insurance mathematics with exercises Hans U. Gerber 2., expanded ed. Berlin u.a. Springer 1995 XV, 217 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematik (DE-588)4037944-9 gnd rswk-swf Lebensversicherung (DE-588)4034928-7 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Lebensversicherung (DE-588)4034928-7 s Versicherungsmathematik (DE-588)4063194-1 s DE-604 Mathematik (DE-588)4037944-9 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006916085&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gerber, Hans U. 1943- Life insurance mathematics with exercises Mathematik (DE-588)4037944-9 gnd Lebensversicherung (DE-588)4034928-7 gnd Versicherungsmathematik (DE-588)4063194-1 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4034928-7 (DE-588)4063194-1 |
| title | Life insurance mathematics with exercises |
| title_alt | Lebensversicherungsmathematik |
| title_auth | Life insurance mathematics with exercises |
| title_exact_search | Life insurance mathematics with exercises |
| title_full | Life insurance mathematics with exercises Hans U. Gerber |
| title_fullStr | Life insurance mathematics with exercises Hans U. Gerber |
| title_full_unstemmed | Life insurance mathematics with exercises Hans U. Gerber |
| title_short | Life insurance mathematics |
| title_sort | life insurance mathematics with exercises |
| title_sub | with exercises |
| topic | Mathematik (DE-588)4037944-9 gnd Lebensversicherung (DE-588)4034928-7 gnd Versicherungsmathematik (DE-588)4063194-1 gnd |
| topic_facet | Mathematik Lebensversicherung Versicherungsmathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006916085&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gerberhansu lebensversicherungsmathematik AT gerberhansu lifeinsurancemathematicswithexercises |