Fundamentals of Actuarial Mathematics

The book is an introduction to actuarial mathematics and features new topics including an introduction to time diagrams and credibility theory, multi-state models and continuous time models.

Inhaltsverzeichnis

Preface.
Acknowledgements.

Notation index.

Part I THE DETERMINISTIC MODEL.

1 Introduction and motivation.

1.1 Risk and insurance.

1.2 Deterministic versus stochastic models.

1.3 Finance and investments.

1.4 Adequacy and equity.

1.5 Reassessment.

1.6 Conclusion.

2 The basic deterministic model.

2.1 Cashflows.

2.2 An analogy with currencies.

2.3 Discount functions.

2.4 Calculating the discount function.

2.5 Interest and discount rates.

2.6 Constant interest.

2.7 Values and actuarial equivalence.

2.8 Regular pattern cashflows.

2.9 Balances and reserves.

2.10 Time shifting and the splitting identity.

2.11 Change of discount function.

2.12 Internal rates of return.

2.13 Forward prices and term structure.

2.14 Standard notation and terminology.

2.15 Spreadsheet calculations.

2.16 Notes and references.

2.17 Exercises.

3 The life table.

3.1 Basic definitions.

3.2 Probabilities.

3.3 Constructing the life table from the values of qx .

3.4 Life expectancy.

3.5 Choice of life tables.

3.6 Standard notation and terminology.

3.7 A sample table.

3.8 Notes and references.

3.9 Exercises.

4 Life annuities.

4.1 Introduction.

4.2 Calculating annuity premiums.

4.3 The interest and survivorship discount function.

4.4 Guaranteed payments.

4.5 Deferred annuities with annual premiums.

4.6 Some practical considerations.

4.7 Standard notation and terminology.

4.8 Spreadsheet calculations.

4.9 Exercises.

5 Life insurance.

5.1 Introduction.

5.2 Calculating life insurance premiums.

5.3 Types of life insurance.

5.4 Combined insurance-annuity benefits.

5.5 Insurances viewed as annuities.

5.6 Summary of formulas.

5.7 A general insurance-annuity identity.

5.8 Standard notation and terminology.

5.9 Spreadsheet applications.

5.10 Exercises.

6 Insurance and annuity reserves.

6.1 Introduction to reserves.

6.2 The general pattern of reserves.

6.3 Recursion.

6.4 Detailed analysis of an insurance or annuity contract.

6.5 Interest and mortality bases for reserves.

6.6 Nonforfeiture values.

6.7 Policies involving a return of the reserve .

6.8 Premium difference and paid-up formulas.

6.9 Universal life and variable annuities.

6.10 Standard notation and terminology.

6.11 Spreadsheet applications.

6.12 Exercises.

7 Fractional durations.

7.1 Introduction.

7.2 Cashflows discounted with interest only.

7.3 Life annuities paid m thly.

7.4 Immediate annuities.

7.5 Approximation and computation.

7.6 Fractional period premiums and reserves.

7.7 Reserves at fractional durations.

7.8 Notes and references.

7.9 Exercises.

8 Continuous payments.

8.1 Introduction to continuous annuities.

8.2 The force of discount.

8.3 The constant interest case.

8.4 Continuous life annuities.

8.5 The force of mortality.

8.6 Insurances payable at the moment of death.

8.7 Premiums and reserves.

8.8 The general insurance-annuity identity in thecontinuous case.

8.9 Differential equations for reserves.

8.10 Some examples of exact calculation.

8.11 Standard actuarial notation and terminology.

8.12 Notes and references.

8.13 Exercises.

9 Select mortality.

9.1 Introduction.

9.2 Select and ultimate tables.

9.3 Changes in formulas.

9.4 Projections in annuity tables.

9.5 Further remarks.

9.6 Exercises.

10 Multiple-life contracts.

10.1 Introduction.

10.2 The joint-life status.

10.3 Joint-life annuities and insurances.

10.4 Last-survivor annuities and insurances.

10.5 Moment of death insurances.

10.6 The general two-life annuity contract.

10.7 The general two-life insurance contract.

10.8 Contingent insurances.

10.9 Duration problems.

10.10 Applications to annuity credit risk.

10.11 Standard notation and terminology.

10.12 Spreadsheet applications.

10.13 Notes and reference

Bericht

"An ideal text for students planning for a professional career asactuaries, providing a solid preparation for the modelingexaminations of the major North American actuarial associations."(Mathematical Reviews, 2011)

"This second edition adds several chapters, including coverageof credibility theory, risk assessment, and multi-state models."(Book News, 1 March 2011)

Produktdetails

• Autoren: S. D. Promislow, S. David Promislow, PROMISLOW S DAVID
• Verlag: Wiley, John and Sons Ltd
• Sprache: Englisch
• Produktform: Fester Einband
• Erschienen: 10.12.2010
• EAN: 9780470684115
• ISBN: 978-0-470-68411-5
• Seiten: 476
• Thema: Naturwissenschaften, Medizin, Informatik, Technik > Mathematik