Life Insurance Mathematics

1 The Mathematics of Compound Interest.- 2 The Future Lifetime of a Life Aged x.- 3 Life Insurance.- 4 Life Annuities.- 5 Net Premiums.- 6 Net Premium Reserves.- 7 Multiple Decrements.- 8 Multiple Life Insurance.- 9 The Total Claim Amount in a Portfolio.- 10 Expense Loadings.- 11 Estimating Probabilities of Death.- Appendix A. Commutation Functions.- A.1 Introduction.- A.2 The Deterministic Model.- A.3 Life Annuities.- A.4 Life Insurance.- A.5 Net Annual Premiums and Premium Reserves.- Appendix B. Simple Interest.- Appendix C. Exercises.- C.0 Introduction.- C.1 Mathematics of Compound Interest: Exercises.- C.1.1 Theory Exercises.- C.1.2 Spreadsheet Exercises.- C.2.1 Theory Exercises.- C.2.2 Spreadsheet Exercises.- C.3 Life Insurance.- C.3.1 Theory Exercises.- C.3.2 Spreadsheet Exercises.- C.4 Life Annuities.- C.4.1 Theory Exercises.- C.4.2 Spreadsheet Exercises.- C.5 Net Premiums.- C.5.1 Notes.- C.5.2 Theory Exercises.- C.5.3 Spreadsheet Exercises.- C.6 Net Premium Reserves.- C.6.1 Theory Exercises.- C.6.2 Spreadsheet Exercises.- C.7 Multiple Decrements: Exercises.- C.7.1 Theory Exercises.- C.8 Multiple Life Insurance: Exercises.- C.8.1 Theory Exercises.- C.8.2 Spreadsheet Exercises.- C.9 The Total Claim Amount in a Portfolio.- C.9.1 Theory Exercises.- C.10 Expense Loadings.- C.10.1 Theory Exercises.- C.10.2 Spreadsheet Exercises.- C.11 Estimating Probabilities of Death.- C.11.1 Theory Exercises.- Appendix D. Solutions.- D.0 Introduction.- D.1 Mathematics of Compound Interest.- D.1.1 Solutions to Theory Exercises.- D.1.2 Solutions to Spreadsheet Exercises.- D.2.1 Solutions to Theory Exercise.- D.2.2 Solutions to Spreadsheet Exercises.- D.3 Life Insurance.- D.3.1 Solutions to Theory Exercises.- D.3.2 Solution to Spreadsheet Exercises.- D.4 Life Annuities.- D.4.1 Solutions to Theory Exercises.- D.4.2 Solutions to Spreadsheet Exercises.- D.5 Net Premiums. Solutions.- D.5.1 Theory Exercises.- D.5.2 Solutions to Spreadsheet Exercises.- D.6 Net Premium Reserves: Solutions.- D.6.1 Theory Exercises.- D.6.2 Solutions to Spreadsheet Exercises.- D.7 Multiple Decrements: Solutions.- D.7.1 Theory Exercises.- D.8 Multiple Life Insurance: Solutions.- D.8.1 Theory Exercises.- D.8.2 Solutions to Spreadsheet Exercises.- D.9 The Total Claim Amount in a Portfolio.- D.9.1 Theory Exercises.- D.10 Expense Loadings.- D.10.1 Theory Exercises.- D.10.2 Spreadsheet Exercises.- D.11 Estimating Probabilities of Death.- D.11.1 Theory Exercises.- Appendix E. Tables.- E.0 Illustrative Life Tables.- E.1 Commutation Columns.- E.2 Multiple Decrement Tables.- References.