Fundamentals of Actuarial Mathematics

• Provides a comprehensive coverage of both the deterministic and stochastic models of life contingencies, risk theory, credibility theory, multi-state models, and an introduction to modern mathematical finance. New edition restructures the material to fit into modern computational methods and provides several spreadsheet examples throughout. Covers the syllabus for the Institute of Actuaries subject CT5, Contingencies * Includes new chapters covering stochastic investments returns, universal life insurance. Elements of option pricing and the Black-Scholes formula will be introduced.

Autorentext

S. David Promislow is the author of Fundamentals of Actuarial Mathematics, 3rd Edition, published by Wiley.

Klappentext
Fundamentals of Actuarial Mathematics provides a comprehensive coverage of both the deterministic and stochastic models of life contingencies, risk theory, credibility theory, multi-state models and an introduction to modern mathematical nance.

• This new edition:*

• Provides an introduction to the mathematics of financial markets, exploring options, risk-neutral evaluation, the fundamental theorem of asset pricing and the Black-Scholes formula.
• Provides coverage of profit testing.
• Presents more in-depth coverage of continuous-time multi-state theory.
• Covers all of the syllabus material on the current life contingencies examinations of the Society of Actuaries, Canadian Institute of Actuaries and the Casualty Actuarial Society (SOA-CIA exams MLC, CSA exam LC), as well as much of the material for SOA-CIA exam C, CAS exam 4, and the British Institute of Actuaries exam CT5.
• Contains a variety of exercises, both computational and theoretical, together with answers, enabling use for self-study.
  Fundamentals of Actuarial Mathematics, 3rd Edition is the ideal text for students planning for a professional career as actuaries, providing a solid preparation for the modelling examinations of major actuarial associations. It also serves as a highly suitable reference for those wanting a sound introduction to the subject, and for those working in insurance, annuities and pensions.

Inhalt

Preface xvii

Acknowledgements xxi

Notation index xxiii

Part I THE DETERMINISTIC LIFE CONTINGENCIES 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 6

1.6 Conclusion 6

2 The basic deterministic model 7

2.1 Cash flows 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 Constant interest 12

2.7 Values and actuarial equivalence 13

2.8 Vector notation 17

2.9 Regular pattern cash flows 18

2.10 Balances and reserves 20

2.11 Time shifting and the splitting identity 26

2.11 Change of discount function 27

2.12 Internal rates of return 28

2.13 Forward prices and term structure 30

2.14 Standard notation and terminology 33

2.15 Spreadsheet calculations 34

Notes and references 35

Exercises 35

3 The life table 39

3.1 Basic definitions 39

3.2 Probabilities 40

3.3 Constructing the life table from the values of qx 41

3.4 Life expectancy 42

3.5 Choice of life tables 44

3.6 Standard notation and terminology 44

3.7 A sample table 45

Notes and references 45

Exercises 45

4 Life annuities 47

4.1 Introduction 47

4.2 Calculating annuity premiums 48

4.3 The interest and survivorship discount function 50

4.4 Guaranteed payments 53

4.5 Deferred annuities with annual premiums 55

4.6 Some practical considerations 56

4.7 Standard notation and terminology 57

4.8 Spreadsheet calculations 58

Exercises 59

5 Life insurance 61

5.1 Introduction 61

5.2 Calculating life insurance premiums 61

5.3 Types of life insurance 64

5.4 Combined insuranceannuity benefits 64

5.5 Insurances viewed as annuities 69

5.6 Summary of formulas 70

5.7 A general insuranceannuity identity 70

5.8 Standard notation and terminology 72

5.9 Spreadsheet applications 74

Exercises 74

6 Insurance and annuity reserves 78

6.1 Introduction to reserves 78

6.2 The general pattern of reserves 81

6.3 Recursion 82

6.4 Detailed analysis of an insurance or annuity contract 83

6.5 Bases for reserves 87

6.6 Nonforfeiture values 88

6.7 Policies involving a return of the reserve 88

6.8 Premium difference and paid-up formulas 90

6.9 Standard notation and terminology 91

6.10 Spreadsheet applications 93

Exercises 94

7 Fractional durations 98

7.1 Introduction 98

7.2 Cash flows discounted with interest only 99

7.3 Life annuities paid

7.4 Immediate annuities 104

7.5 Approximation and computation 105

7.6 Fractional period premiums and reserves 106

7.7 Reserves at fractional durations 107

7.8 Standard notation and terminology 109

Exercises 109

8 Continuous payments 112

8.1 Introduction to continuous annuities 112

8.2 The force of discount 113

8.3 The constant interest case 114

8.4 Continuous life annuities 115

8.5 The force of mortality 118

8.6 Insurances payable at the moment of death 119

8.7 Premiums and reserves 122

8.8 The general insuranceannuity identity in the continuous case 123

8.9 Differential equations for reserves 124 8.10 Some examp...