Fundamentals of actuarial mathematics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester
Wiley
2006
|
| Subjects: | |
| Online Access: | Table of contents Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIX, 372 S. |
| ISBN: | 0470016892 9780470016893 |
Staff View
MARC
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| 100 | 1 | |a Promislow, S. David |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fundamentals of actuarial mathematics |c S. David Promislow |
| 264 | 1 | |a Chichester |b Wiley |c 2006 | |
| 300 | |a XIX, 372 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Assurance - Mathématiques | |
| 650 | 4 | |a Mathématiques financières | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Insurance |x Mathematics | |
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Record in the Search Index
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| adam_text | Contents
Preface xiii
Notation index xvii
PART I THE DETERMINISTIC MODEL 1
1 Introduction and motivation 3
1.1 Risk and insurance 3
1.2 Deterministic versus stochastic models 4
1.3 Finance and investments 5
1.4 Adequacy and equity 5
1.5 Reassessment 5
1.6 Conclusion 6
2 The basic deterministic model 7
2.1 Cashflows 7
2.2 An analogy with currencies 8
2.3 Discount functions 9
2.4 Calculating the discount function 11
2.5 Interest and discount rates 12
2.6 The constant interest case 12
2.7 Values and actuarial equivalence 13
2.8 The case of equal cashflows 17
2.9 Balances and reserves 18
2.10 Time shifting and the splitting identity 24
*2.11 Change of discount function 25
*2.12 Internal rate of return 26
2.13 Standard notation and terminology 28
2.14 Spreadsheet calculations 30
2.15 Notes and references 32
Exercises 32
3 The life table 37
3.1 Basic definitions 37
3.2 Probabilities 38
viii Contents
3.3 Constructing the life table from the values of qx 39
3.4 Life expectancy 40
3.5 Choice of life tables 42
3.6 Standard notation and terminology 42
3.7 A sample table 43
3.8 Notes and references 43
Exercises 43
4 Life annuities 45
4.1 Introduction 45
4.2 Calculating annuity premiums 46
4.3 The interest and survivorship discount function 48
4.4 Guaranteed payments 51
4.5 Deferred annuities with annual premiums 52
4.6 Some practical considerations 53
4.7 Standard notation and terminology 54
4.8 Spreadsheet calculations 55
Exercises 56
5 Life insurance 59
5.1 Introduction 59
5.2 Calculating life insurance premiums 59
5.3 Types of life insurance 61
5.4 Combined benefits 62
5.5 Insurances viewed as annuities 65
5.6 Summary of formulas 66
5.7 A general insurance annuity identity 66
5.8 Standard notation and terminology 68
5.9 Spreadsheet applications 70
Exercises 70
6 Insurance and annuity reserves 75
6.1 Introduction to reserves 75
6.2 The general pattern of reserves 77
6.3 Recursion 78
6.4 Detailed analysis of an insurance or annuity contract 79
6.5 Bases for reserves 82
6.6 Nonforfeiture values 83
6.7 Policies involving a return of the reserve 84
6.8 Premium difference and paid up formulas 85
6.9 Standard notation and terminology 87
6.10 Spreadsheet applications 89
Exercises 90
7 Fractional durations 95
7.1 Introduction 95
7.2 Cashflows discounted with interest only 96
7.3 Life annuities paid mthly 98
Contents ix
7.4 Immediate annuities 100
7.5 Approximation and computation 101
7.6 Fractional period premiums and reserves 103
7.7 Reserves at fractional durations 104
7.8 Notes and references 105
Exercises 106
8 Continuous payments 109
8.1 Introduction to continuous annuities 109
8.2 The force of discount 110
8.3 The constant interest case 111
8.4 Continuous life annuities 112
8.5 The force of mortality 114
8.6 Insurances payable at the moment of death 116
8.7 Premiums and reserves 118
8.8 The general insurance annuity identity in the continuous case 119
8.9 Differential equations for reserves 120
8.10 Some examples of exact calculation 121
8.11 Standard notation and terminology 124
8.12 Notes and references 124
Exercises 125
9 Select mortality 129
9.1 Introduction 129
9.2 Select and ultimate tables 130
9.3 Changes in formulas 131
9.4 Further remarks 133
Exercises 133
10 Multiple life contracts 135
10.1 Introduction 135
10.2 The joint life status 135
10.3 Joint life annuities and insurances 137
10.4 Last survivor annuities and insurances 138
10.5 Moment of death insurances 139
10.6 The general two life annuity contract 140
10.7 The general two life insurance contract 142
10.8 Contingent insurances 143
10.9 Standard notation and terminology 146
10.10 Spreadsheet applications 146
10.11 Notes and references 147
Exercises 47
11 Multiple decrement theory 151
11.1 Introduction 151
11.2 The basic model 151
11.3 Insurances 154
x Contents
11.4 Determining the model from the forces of decrement 155
11.5 The analogy with joint life statuses 156
11.6 A machine analogy 156
11.7 Associated single decrement tables 159
11.8 Notes and references 161
Exercises 161
12 Expenses 165
12.1 Introduction 165
12.2 Effect on reserves 167
12.3 Realistic reserve and balance calculations 168
12.4 Notes and references 169
Exercises 169
PART II THE STOCHASTIC MODEL 171
13 Survival distributions and failure times 173
13.1 Introduction to survival distributions 173
13.2 The discrete case 174
13.3 The continuous case 175
13.4 Examples 177
13.5 Shifted distributions 178
13.6 The standard approximation 179
13.7 The stochastic life table 181
13.8 Life expectancy in the stochastic model 182
13.9 Notes and references 183
Exercises 184
14 The stochastic approach to insurance and annuities 187
14.1 Introduction 187
14.2 The stochastic approach to insurance benefits 188
14.3 The stochastic approach to annuity benefits 191
14.4 Deferred contracts 194
14.5 The stochastic approach to reserves 195
14.6 The stochastic approach to premiums 196
14.7 The variance of rL 199
14.8 Standard notation and terminology 202
14.9 Notes and references 202
Exercises 202
15 Simplifications under constant benefit contracts 207
15.1 Introduction 207
15.2 Variance calculations in the continuous case 207
15.3 Variance calculations in the discrete case 209
15.4 Exact distributions 210
15.5 Some nonconstant benefit examples 212
Exercises 214
Contents xi
16 The minimum failure time 217
16.1 Introduction 217
16.2 Joint distributions 217
16.3 The distribution of T 219
16.4 The joint distribution of (T, J) 220
16.5 Approximations 228
16.6 Other problems 234
16.7 The common shock model 234
16.8 Copulas 237
16.9 Notes and references 239
Exercises 240
PART III RISK THEORY 243
17 Compound distributions 245
17.1 Introduction 245
17.2 The mean and variance of S 247
17.3 Generating functions 248
17.4 Exact distribution of S 249
17.5 Choosing a frequency distribution 250
17.6 Choosing a severity distribution 253
17.7 Handling the point mass at 0 256
17.8 Counting claims of a particular type 257
17.9 The sum of two compound Poisson distributions 259
17.10 Deductibles and other modifications 260
17.11 A recursion formula for 5 265
17.12 Notes and references 270
Exercises 270
18 An introduction to stochastic processes 275
18.1 Introduction 275
18.2 Markov chains 277
18.3 Examples 278
18.4 Martingales 280
18.5 Finite state Markov chains 281
18.6 Multi state insurances and annuities 288
18.7 Notes and references 291
Exercises 291
19 Poisson processes 295
19.1 Introduction 295
19.2 Definition of a Poisson process 296
19.3 Waiting times 297
19.4 Some properties of the Poisson process 298
19.5 Nonhomogeneous Poisson processes 299
xii Contents
19.6 Compound Poisson processes 300
19.7 Notes and references 300
Exercises 301
20 Ruin models 305
20.1 Introduction 305
20.2 A functional equation approach 306
20.3 The martingale approach to ruin theory 309
20.4 Distribution of the deficit at ruin 317
20.5 Recursion formulas 318
20.6 The compound Poisson surplus process 322
20.7 The maximal aggregate loss 325
20.8 Notes and references 329
Exercises 329
Appendix A review of probability theory 333
A. 1 Introduction 333
A.2 Sample spaces and probability measures 333
A.3 Conditioning and independence 335
A.4 Random variables 335
A.5 Distributions 336
A.6 Expectations and moments 337
A.7 Expectation in terms of the distribution function 338
A.8 Joint distributions 339
A.9 Conditioning and independence for random variables 340
A. 10 Convolution 342
A. 11 Moment generating functions 346
A. 12 Probability generating functions 349
A. 13 Mixtures 350
Answers to exercises 353
References 367
Index 369
|
| adam_txt |
Contents
Preface xiii
Notation index xvii
PART I THE DETERMINISTIC MODEL 1
1 Introduction and motivation 3
1.1 Risk and insurance 3
1.2 Deterministic versus stochastic models 4
1.3 Finance and investments 5
1.4 Adequacy and equity 5
1.5 Reassessment 5
1.6 Conclusion 6
2 The basic deterministic model 7
2.1 Cashflows 7
2.2 An analogy with currencies 8
2.3 Discount functions 9
2.4 Calculating the discount function 11
2.5 Interest and discount rates 12
2.6 The constant interest case 12
2.7 Values and actuarial equivalence 13
2.8 The case of equal cashflows 17
2.9 Balances and reserves 18
2.10 Time shifting and the splitting identity 24
*2.11 Change of discount function 25
*2.12 Internal rate of return 26
2.13 Standard notation and terminology 28
2.14 Spreadsheet calculations 30
2.15 Notes and references 32
Exercises 32
3 The life table 37
3.1 Basic definitions 37
3.2 Probabilities 38
viii Contents
3.3 Constructing the life table from the values of qx 39
3.4 Life expectancy 40
3.5 Choice of life tables 42
3.6 Standard notation and terminology 42
3.7 A sample table 43
3.8 Notes and references 43
Exercises 43
4 Life annuities 45
4.1 Introduction 45
4.2 Calculating annuity premiums 46
4.3 The interest and survivorship discount function 48
4.4 Guaranteed payments 51
4.5 Deferred annuities with annual premiums 52
4.6 Some practical considerations 53
4.7 Standard notation and terminology 54
4.8 Spreadsheet calculations 55
Exercises 56
5 Life insurance 59
5.1 Introduction 59
5.2 Calculating life insurance premiums 59
5.3 Types of life insurance 61
5.4 Combined benefits 62
5.5 Insurances viewed as annuities 65
5.6 Summary of formulas 66
5.7 A general insurance annuity identity 66
5.8 Standard notation and terminology 68
5.9 Spreadsheet applications 70
Exercises 70
6 Insurance and annuity reserves 75
6.1 Introduction to reserves 75
6.2 The general pattern of reserves 77
6.3 Recursion 78
6.4 Detailed analysis of an insurance or annuity contract 79
6.5 Bases for reserves 82
6.6 Nonforfeiture values 83
6.7 Policies involving a return of the reserve 84
6.8 Premium difference and paid up formulas 85
6.9 Standard notation and terminology 87
6.10 Spreadsheet applications 89
Exercises 90
7 Fractional durations 95
7.1 Introduction 95
7.2 Cashflows discounted with interest only 96
7.3 Life annuities paid mthly 98
Contents ix
7.4 Immediate annuities 100
7.5 Approximation and computation 101
7.6 Fractional period premiums and reserves 103
7.7 Reserves at fractional durations 104
7.8 Notes and references 105
Exercises 106
8 Continuous payments 109
8.1 Introduction to continuous annuities 109
8.2 The force of discount 110
8.3 The constant interest case 111
8.4 Continuous life annuities 112
8.5 The force of mortality 114
8.6 Insurances payable at the moment of death 116
8.7 Premiums and reserves 118
8.8 The general insurance annuity identity in the continuous case 119
8.9 Differential equations for reserves 120
8.10 Some examples of exact calculation 121
8.11 Standard notation and terminology 124
8.12 Notes and references 124
Exercises 125
9 Select mortality 129
9.1 Introduction 129
9.2 Select and ultimate tables 130
9.3 Changes in formulas 131
9.4 Further remarks 133
Exercises 133
10 Multiple life contracts 135
10.1 Introduction 135
10.2 The joint life status 135
10.3 Joint life annuities and insurances 137
10.4 Last survivor annuities and insurances 138
10.5 Moment of death insurances 139
10.6 The general two life annuity contract 140
10.7 The general two life insurance contract 142
10.8 Contingent insurances 143
10.9 Standard notation and terminology 146
10.10 Spreadsheet applications 146
10.11 Notes and references 147
Exercises '47
11 Multiple decrement theory 151
11.1 Introduction 151
11.2 The basic model 151
11.3 Insurances 154
x Contents
11.4 Determining the model from the forces of decrement 155
11.5 The analogy with joint life statuses 156
11.6 A machine analogy 156
11.7 Associated single decrement tables 159
11.8 Notes and references 161
Exercises 161
12 Expenses 165
12.1 Introduction 165
12.2 Effect on reserves 167
12.3 Realistic reserve and balance calculations 168
12.4 Notes and references 169
Exercises 169
PART II THE STOCHASTIC MODEL 171
13 Survival distributions and failure times 173
13.1 Introduction to survival distributions 173
13.2 The discrete case 174
13.3 The continuous case 175
13.4 Examples 177
13.5 Shifted distributions 178
13.6 The standard approximation 179
13.7 The stochastic life table 181
13.8 Life expectancy in the stochastic model 182
13.9 Notes and references 183
Exercises 184
14 The stochastic approach to insurance and annuities 187
14.1 Introduction 187
14.2 The stochastic approach to insurance benefits 188
14.3 The stochastic approach to annuity benefits 191
14.4 Deferred contracts 194
14.5 The stochastic approach to reserves 195
14.6 The stochastic approach to premiums 196
14.7 The variance of rL 199
14.8 Standard notation and terminology 202
14.9 Notes and references 202
Exercises 202
15 Simplifications under constant benefit contracts 207
15.1 Introduction 207
15.2 Variance calculations in the continuous case 207
15.3 Variance calculations in the discrete case 209
15.4 Exact distributions 210
15.5 Some nonconstant benefit examples 212
Exercises 214
Contents xi
16 The minimum failure time 217
16.1 Introduction 217
16.2 Joint distributions 217
16.3 The distribution of T 219
16.4 The joint distribution of (T, J) 220
16.5 Approximations 228
16.6 Other problems 234
16.7 The common shock model 234
16.8 Copulas 237
16.9 Notes and references 239
Exercises 240
PART III RISK THEORY 243
17 Compound distributions 245
17.1 Introduction 245
17.2 The mean and variance of S 247
17.3 Generating functions 248
17.4 Exact distribution of S 249
17.5 Choosing a frequency distribution 250
17.6 Choosing a severity distribution 253
17.7 Handling the point mass at 0 256
17.8 Counting claims of a particular type 257
17.9 The sum of two compound Poisson distributions 259
17.10 Deductibles and other modifications 260
17.11 A recursion formula for 5 265
17.12 Notes and references 270
Exercises 270
18 An introduction to stochastic processes 275
18.1 Introduction 275
18.2 Markov chains 277
18.3 Examples 278
18.4 Martingales 280
18.5 Finite state Markov chains 281
18.6 Multi state insurances and annuities 288
18.7 Notes and references 291
Exercises 291
19 Poisson processes 295
19.1 Introduction 295
19.2 Definition of a Poisson process 296
19.3 Waiting times 297
19.4 Some properties of the Poisson process 298
19.5 Nonhomogeneous Poisson processes 299
xii Contents
19.6 Compound Poisson processes 300
19.7 Notes and references 300
Exercises 301
20 Ruin models 305
20.1 Introduction 305
20.2 A functional equation approach 306
20.3 The martingale approach to ruin theory 309
20.4 Distribution of the deficit at ruin 317
20.5 Recursion formulas 318
20.6 The compound Poisson surplus process 322
20.7 The maximal aggregate loss 325
20.8 Notes and references 329
Exercises 329
Appendix A review of probability theory 333
A. 1 Introduction 333
A.2 Sample spaces and probability measures 333
A.3 Conditioning and independence 335
A.4 Random variables 335
A.5 Distributions 336
A.6 Expectations and moments 337
A.7 Expectation in terms of the distribution function 338
A.8 Joint distributions 339
A.9 Conditioning and independence for random variables 340
A. 10 Convolution 342
A. 11 Moment generating functions 346
A. 12 Probability generating functions 349
A. 13 Mixtures 350
Answers to exercises 353
References 367
Index 369 |
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| publisher | Wiley |
| record_format | marc |
| spelling | Promislow, S. David Verfasser aut Fundamentals of actuarial mathematics S. David Promislow Chichester Wiley 2006 XIX, 372 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Assurance - Mathématiques Mathématiques financières Mathematik Insurance Mathematics Business mathematics Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Versicherungsmathematik (DE-588)4063194-1 s DE-604 http://www.loc.gov/catdir/toc/ecip061/2005028319.html Table of contents http://www.loc.gov/catdir/enhancements/fy0623/2005028319-d.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014802480&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Promislow, S. David Fundamentals of actuarial mathematics Assurance - Mathématiques Mathématiques financières Mathematik Insurance Mathematics Business mathematics Versicherungsmathematik (DE-588)4063194-1 gnd |
| subject_GND | (DE-588)4063194-1 (DE-588)4123623-3 |
| title | Fundamentals of actuarial mathematics |
| title_auth | Fundamentals of actuarial mathematics |
| title_exact_search | Fundamentals of actuarial mathematics |
| title_exact_search_txtP | Fundamentals of actuarial mathematics |
| title_full | Fundamentals of actuarial mathematics S. David Promislow |
| title_fullStr | Fundamentals of actuarial mathematics S. David Promislow |
| title_full_unstemmed | Fundamentals of actuarial mathematics S. David Promislow |
| title_short | Fundamentals of actuarial mathematics |
| title_sort | fundamentals of actuarial mathematics |
| topic | Assurance - Mathématiques Mathématiques financières Mathematik Insurance Mathematics Business mathematics Versicherungsmathematik (DE-588)4063194-1 gnd |
| topic_facet | Assurance - Mathématiques Mathématiques financières Mathematik Insurance Mathematics Business mathematics Versicherungsmathematik Lehrbuch |
| url | http://www.loc.gov/catdir/toc/ecip061/2005028319.html http://www.loc.gov/catdir/enhancements/fy0623/2005028319-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014802480&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT promislowsdavid fundamentalsofactuarialmathematics |