Intro -- Fundamentals of Actuarial Mathematics -- Contents -- Preface -- Acknowledgements -- About the companion website -- Part I THE DETERMINISTIC LIFE CONTINGENCIES 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 Cash flows -- 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 Vector notation -- 2.9 Regular pattern cash flows -- 2.10 Balances and reserves -- 2.10.1 Basic concepts -- 2.10.2 Relation between balances and reserves -- 2.10.3 Prospective versus retrospective methods -- 2.10.4 Recursion formulas -- 2.11 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 -- 2.14.1 Standard notation for cash flows discounted with interest -- 2.14.2 New notation
2.15 Spreadsheet calculations -- Notes and references -- 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 -- Notes and references -- Exercises -- 4 Life annuities -- 4.1 Introduction -- 4.2 Calculating annuity premiums -- 4.3 The interest and survivorship discount function -- 4.3.1 The basic definition -- 4.3.2 Relations between yx for various values of x -- 4.4 Guaranteed payments
4.5 Deferred annuities with annual premiums -- 4.6 Some practical considerations -- 4.6.1 Gross premiums -- 4.6.2 Gender aspects -- 4.7 Standard notation and terminology -- 4.8 Spreadsheet calculations -- 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 -- 5.7.1 The general identity -- 5.7.2 The endowment identity -- 5.8 Standard notation and terminology
5.8.1 Single-premium notation -- 5.8.2 Annual-premium notation -- 5.8.3 Identities -- 5.9 Spreadsheet applications -- 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 -- 6.4.1 Gains and losses -- 6.4.2 The risk-savings decomposition -- 6.5 Bases for reserves -- 6.6 Nonforfeiture values -- 6.7 Policies involving a return of the reserve -- 6.8 Premium difference and paid-up formulas -- 6.8.1 Premium difference formulas -- 6.8.2 Paid-up formulas
